All that is green west of the Rockies quivers before that most fearsome of Mormon beasts, the Mormon cricket. It wasn’t always so. Before the 1870s (in the Anglo-European world), mesch, “a curious kind of cricket,” “an ugly cricket,” “a large kind of cricket,” the “mountain cricket” ravaged the left side of the American map.  Colonel Kane and the Mormons described it:
Wingless, dumpy, black, swollen-headed, with bulging eyes in cases like goggles, mounted upon legs of steel wire and clock-spring, and with a general personal appearance that justified the Mormons in comparing him to a cross of the spider on the Buffalo, the Deseret cricket comes down from the mountains at a certain season of the year, in voracious and desolating myriads. 
As you’ve probably grown tired of hearing, the Mormon cricket isn’t really a cricket. It’s a katydid sporting the genus name Anabrus, “in allusion to [its] unprepossessing appearance”; an + abroV = “not soft, delicate, tender, dainty, or beautiful,” which I think fits pretty well.  (Image: A. simplex cannibalizes )
In the latter nineteenth century, A. simplex and Mormons went together, bound in place by the “miracle(s) of the gulls.”  Mormons touted the birds and beasts—though not necessarily the 1848 models—at least as early as 1849, while visitors and anti-Mormons reported or attacked the “miracle” and scientists enlivened reports with it. , ,  Conversely, Mormon preaching employed the defoliating swarms as a conditionally eminent scourge. 
Edibility was the other thing that made Anabrus famous in the nineteenth century. As California gulls and Native American Peoples knew, a good chunk of the pillaged greenery ended up as handy, if jumpy, protein-nuggets. If Anglo-Europeans weren’t so persnickety about six-legged food, they wouldn’t have derided the Indians so much and the miracle might have been very different.  To wit: the Lord sent gulls to protect the crops but also crickets for hungry Saints to eat. Maybe. 
Unlike the other animal names I’ve been studying, the Mormons themselves (with help from anti-Mormons) probably bear most responsibility for the name, “Mormon cricket.” The prominence given the miracle kept the association between Mormons and A. simplex in the public eye and eventually the name stuck. Also unlike some of the other names, “Mormon cricket” seems to have carried less pejorative intent—though the name did not seem to catch on in Utah until much later than elsewhere and the timing of its rise in popularity coincided with the big anti-polygamy push in the 1880s and 90s.
Of course, it makes one wonder when the “Black Phillistines”—that “mo[w] their way even with the ground, leaving it as if touched with an acid or burnt by fire,” that have “an eagle-eyed, staring appearance” suggesting “that [they] may be the habitation of a vindictive little demon”—get called “Mormon,” while the closest competition for neighborhood bully goes by “Idaho devil.” 
Happy Pioneer Day!
Unidentified gull trying to eat unidentified starfish, © Begim.com
Bonus rant: I spent an irresponsible amount of time looking for a photograph of a California gull upchucking a Mormon cricket exoskeleton and I failed. I couldn’t even find a photo of said gull eating said cricket. The inaccessibility of images illustrating such an important part of Mormon zoological history is scandalous. (That, or my search skills are weak.)
The standard caveats: When I write “The earliest instance…” or similar, the “that I’ve found to date” is implied. When I write something like “Most of the Mormon records used…”I am reporting a non-quantitative, subjective impression (unless otherwise stated).
 The earliest “Mormon cricket” I’ve found comes from an 1878 hunting manual. Reporting that badgers are “very fond” of them. Joseph H Batty, How to Hunt and Trap, Containing Full Instruction for Hunting the Buffalo, Elk… (New York: Albert Cogswell, 1878) p178. The Shoshone or Snake Indians knew A. simplex as mesch. JD Putnam, “Report on the Insects collected by Captain Jones’ Expedition to Northwestern Wyoming in 1873,” Proceedings of the Davenport Academy of Natural Sciences, vol 1: 1867-1876 (Davenport, Iowa: Women’s Centennial Association, 1876), 192; “They are known by several common names, among which are great plains cricket, western cricket, war cricket, army cricket, mormon cricket, Idaho cricket, coulee cricket, and Idaho devil.” Some of the names also apply to other species. Caudell, “The Decticinae of North America,” Proceedings of the United States National Museum 32 (1907):351. “Curious”: Benjamin G. Ferris, Utah and the Mormons: The History, Government, Doctrines, Customs, and Prospects of the Latter-day Saints (New York: Harper and Brothers, 1856) p159; “Ugly”: Mrs. Benjamin G. Ferris, The Mormons at Home with Some Incidents of Travel from Missouri to California, 1852-3 (New York: Dix & Edwards, 1856) p106-7; “Large”: Charles Knight, “Utah,” The Second Supplement to the Penny Cyclopaedia of the Society for the Diffusion of Useful Knowledge (London: Knight, 1858) p712.
 cmonks, “MORMON CRICKETS!,” UtterWonder.com, posted 2006 Apr 26. The caption reads: “Hey there! Do you have a relationship with your savior? No? Well, would you like some information about the one, true church? Not interested? Okay, then, I’ll just eat you instead. Sinner!”
 Band name, anyone? Thomas L Kane, “The Mormons, A Discourse Delivered before the Historical Society of Pennsylvania, March 26, 1850,” Pamphlet (Philadelphia: King & Baird, 1850): 66. Many organs, both Mormon and non-, reprinted or excerpted or plagiarized TL Kane’s 1850 speech. For two of many examples: Eliakim Littell, Robert S Littell, Littell’s Living Age 26 (Boston, 1850 Jul-Sep): 297; Thomas L. Kane, “The Mormons…,” Millennial Star 13 no 12 (1851 Jun 15): 178.
In an 1896 article, the spider/buffalo idea transmuted: “Among the Mormons, who suffered grievously from this pest, a belief was current formerly that the grasshopper was a cross between the spider and the buffalo.” No author listed, “Bugs, Worms, and Beetles,” New York Times, 1896 Jul 13, p7. RF Burton rehashed Kane’s description in City of the Saints, and Across the Rocky Mountains to California (New York: Harper & Brothers, 1862), p284.
 SS Haldeman, “Insects,” in Appendix C, “Zoology” of Documents Printed by Order of the Senate of the United States During the Special Session of the Senate Begun and Held at the City of Washington, March 4, 1851 (Washington: A Boyd Hamilton, 1851) v2 p371-2.
 William G. Hartley, “Mormons, Crickets, and Gulls: A New Look at an Old Story,” Utah Historical Quarterly 38 (Summer 1970): 224-39. Also available in: D. Michael Quinn, ed., The New Mormon History: Revisionist Essays on the Past (Salt Lake City: Signature Books, 1992), 137-152; David B. Madsen and Brigham D. Madsen, “One Man’s Meat Is Another Man’s Poison: A Revisionist View of the Seagull ‘Miracle,'” Nevada Historical Quarterly 30 (1987): 165-181; also available in John S. McCormick and John R. Sillito, eds., A World We Thought We Knew: Readings in Utah History (Salt Lake City: University of Utah Press, 1995), p. 52-67.
 “The crickets have not troubled us any this year. Hundreds and thousands of gulls made their appearance early in the Spring, and…have swept them clean, so that there is scarce a cricket to be found in the valley. [¶] We look upon this as one of the manifestations of the Almighty, for the mountaineers say that they never found gulls here till the Mormons come. …This is plainly a miracle in behalf of this people, as the sending of the quails in the camp of the Israelites….” Letter from the First Presidency, Great Salt Lake City, 1849 Jul 16, quoted in Kane, “The Mormons,” 66-7.
 “He [Mormon speaker] gave quite a graphic description of the destruction which threatened their first crops, by the ravages of an ugly cricket, until the ravagers were in turn destroyed by flocks of white gulls, which came over the mountain tops—a thing which, he assured us, had never before been seen. Mr. F[erris, her husband]. asked him where they came from. That, he said, was a mystery—he did not doubt they were created for the occasion. The man is a Jesuit, after all. …I could see him slyly watching the effect the narrative might have upon his audience.” Mrs. Benjamin G. Ferris, The Mormons at Home with Some Incidents of Travel from Missouri to California, 1852-3 (New York: Dix & Edwards, 1856) p106-7; “We can hardly wonder that the Mormons…should have seen in this natural phenomenon a miracle…or accuse them, as anti-Mormons have done, of forging signs and portents.” Burton, City of the Saints, 284.
 “Mr. James McKnight…states that when …this cricket appeared in immense swarms, destroying their whole crops …providentially, or miraculously, as it was deemed by the Mormons, vast flocks of white gulls suddenly appeared and destroyed the crickets…. Since that time these birds are held almost sacred in Utah.” Townend Glover, “Report of the Entomologist and Curator of the Museum,” in Frederick Watts, Report of the Commissioner of Agriculture for the Year 1871 (Washington: Government Printing Office, 1872) p79.
 “When this people are blessed so much that they consider their blessings a burden and a drudge to them, you may always calculate on a cricket war, a grasshopper war, a drought, too much rain, or something else to make the scales preponderate the other way.” Brigham Young, speech in Salt Lake City, 1853 Jun 05, Journal of Discourses 1.250.
 I generalize from my computer searches and from the quotations in Hartley, “Mormons, Crickets, and Gulls.”
 First Presidency Letter, 1849 Oct 12, as quoted in Kane, “The Mormons,” p81; Anson Call, as quoted in Edward W Tullidge, Tullidge’s Histories, Volume II, Containing the History of All the Northern, Eastern and Western Counties of Utah; Also the Counties of Southern Idaho (Salt Lake City: Juvenile Instructor, 1889) p63; No author listed, “What Men Say of the City of the Saints,” Millennial Star 65 no 20 (1903 May 14): 308; Robert Mullen, The Latter-Day Saints: The Mormons Yesterday and Today (New York: Doubleday, 1966) p139; Thomas G Alexander, Utah, the Right Place: The Official Centennial History (Salt Lake City: Gibbs Smith, 1995) p103.
 Note that both authors here are Utah residents. “‘Army crickets’ they were called, because they did not fly, but marched.” Howard R Driggs, Live Language Lessons, Second Book (Chicago: University Publishing Co, 1917) p106; “…poorest crop outlook in years, due to grasshopper infestation, large army crickets, wild bees and drouth.” “Honey Markets,” Gleanings in Bee Culture 50 no 9 (1922 Sep):560. “Deseret crickets” appear frequently, and “cricket-locusts” less so, but both almost always quoting Kane, “The Mormons,” 66-7; “Die Mormonen nannten diese gefräbigen Thiere ‘Deseret Crickets.’” [The Mormons call these ravenous animals ‘Deseret Crickets.’] Theodor Olshausen, Geschichte der Mormonen, oder, Jüngsten-Tages-Heiligen in Nordamerika (Göttingen: Bandenhoect und Ruprecht, 1856) p149.
 Quoted from the Deseret News in “Minutes of the Semi-Annual Conference of the Church of Jesus Christ of Latter-day Saints,” Millennial Star 19 no 8 (1857 Feb 21):115. I have not yet identified the song music or text. But boy howdy would I like to.
 The first instance I’ve noticed dates to 1910. The reference is a no-preview on gbooks: Improvement Era (1910): 100, “… among which “Western Cricket” and “Mormon Cricket” are common. This is undoubtedly the insect of the plague incident to pioneer days. …” Even this usage merely acknowledges alternate names.
 Please note that “Digger Indian” is derogatory and should not be used to indicate the Goshute or Paiute groups. “The Digger Indians, inhabiting the Great Basin, are of the very lowest form of humanity. Dispersed in single families, without fire-arms, eating seeds and insects and digging roots (and hence their name)….” DeWitt Clinton Peters, Pioneer life and frontier adventures: An Authentic Record of the Romantic Life and Daring Exploits of Kit Carson and His Companions, from his own narrative (Boston: Estes and Lauriat, 1881), 223; “In natural conformation the Digger Indian is very few degrees removed from the ouran-outang [orangutan]; not much above its stature, having the same compressed physiognomy, a low forehead, with little or no space between the eyebrows and roots of the hair. …They exist, as their name denotes, on roots dug from the earth, vermin and crickets; …such is their inherent sloth, that they have been known to die of absolute inanition rather than make an effort to obtain food.” William Kelly, Across the Rocky Mountains, from New York to California: With a Visit to the Celebrated Mormon Colony at the Great Salt Lake (London: Simms and McIntyre, 1852), 178.
 Madsen and. Madsen, “One Man’s Meat Is Another Man’s Poison” Nevada Historical Quarterly 30 (1987): 165-181.
 Kane, “Mormons,” 66; Call, quoted in Tullidge’s Histories, 63.
“We learn from the New York Herald that the crickets and grasshoppers are devouring up, and serve them right, the Mormons of Utah. That grasshoppers will devour men, nay, whole families alive, is a fact not to be denied by any one who will consider the doings of the Gresham grasshopper at the Stock Exchange. How many a broker has that grasshopper nibbled to bits, singing the while, and Bow bells ringing music to the feast! In like manner, the Mormons were chewed up in the Illinois in 1846, devoured —say the accounts—‘by the crickets; great goggle-eyed, crook-legged, bottle-bodied monsters.’ They are more than a match for the oriental white ant, that in a night will leave the bones of an elephant as clean as a domino. Most appalling are the accounts of the ravages of these monster crickets on the hearths of the Mormons. Cradles, with half-a-dozen babies in them at night, are found empty in the morning. And a doting and incomparable husband—the spouse of fourteen wives at dewy eve—finds himself seven times a widower at sunrise. It is said, and we give the fact as a warning to all about to emigrate to marry at the Salt Lake, that, the crickets have a preference for wives; carrying half-a-dozen off from under one roof, and devouring them to a music of their own, and that may be set to the old words of—‘Plenty more where they come from.'” “The Cricket on the Mormon’s Hearth,” Punch, or the London Charivari 29 (1855 Sep 01):86.