Mormon missionary efforts within the United States prompted resentment beyond simple sectarianism. Most turn-of-the-century Americans thought of “missionaries” as working with non-White non-Protestants, usually overseas.  Since they sent missionaries to “inferiors” they tended to perceive missionaries at their own door as a racial insult.
In other words, the mere presence of Mormon missionaries sometimes communicated, “You are neither White nor Christian.” For example, Elder Clark:
one woman ordered us out of her house when She found we were Mormon and said ‘we are not Heathens’ and said ‘you can go over there where that negro family is and talk to them.’ I said Some of negros was better than the whites She said go I don’t want anything to do with Mormons.” 
In the latter 1800s, “heathen” usually marked a serious, if not necessarily rigorous, anthropological, theological, and imperial category; see, for example, Rudyard Kipling’s “The White Man’s Burden.”  Six entries in the diaries use “heathen.” Four, all from Elder Clark, quote non-Mormons resisting the perceived implication of heathenism.  The other two, from Jones and Clark when denied lodging, make it explicit. 
I don’t know how widespread, Mormon-specific, bilateral, or significant the racial valences of domestic missions were. In the shadow of polygamy and violence, home missions might have been almost invisible. Five of six “heathens” come from one diary, so there’s probably a personality or location factor, and six (out of four thousand) isn’t very many anyway. I haven’t noticed other ways of expressing the idea in the diaries.
Non-Mormons often treated the Elders just like other traveling ministers, so “racial insult” was probably not the dominant paradigm. The Elders tended to describe what they did as “teaching the Gospel of Jesus Christ” and they sometimes criticized other religions vehemently, so there is some basis for imagining the Elders as arrogant imperial agents.
The “Southwestern States Mission” series uses the diaries of six missionaries who served in eastern Texas around 1900 to illustrate aspects of Mormon material culture, lived religion, and social History. The missionaries are Mission President Duffin and Elders Brooks, Clark, Folkman, Forsha, and Jones. The series is inspired by Ardis Parshall’s serial posting of the missionary diary of Willard Larson Jones at Keepapitchinin. Previous installment here.
 Various groups contest(ed) words like “Christian,” and “White,” “American.” To avoid having half the post in scare quotes, I acknowledge the contestation here.
I probably shouldn’t have put “Home Missions” in the title; the usage is ahistorical. I don’t know what, if anything, Mormons at the time called Missions in the US, but the “home missionary program” was what they did in the Mormon Culture Region.
Protestants did have missions in Utah, but their management, discussion, and financing were of a piece with the foreign missions: Protestant missions in Utah denigrated Mormon Whiteness, Christianity, and American-ness. I (and others) have argued elsewhere that exchanges of missionaries can, with profit, be imagined as acts of empire. American and European imperialists used missionary work as both pre and post hoc justifications for their actions. An intrinsic part of “the white man’s burden” was to “better” subjugated peoples, part of which was accomplished by sponsoring missionaries.
 Clark, 1901 Feb 15 Fri.
 Of course, it’s a long way from rural Texas to literary England, but I think the usages were consistent. Incidentally, Kipling’s “Recessional” also used “heathen” and is in the 1985 LDS hymnal (though without the “heathen” stanza; #80, “God of Our Fathers, Known of Old”). The Mormon hymn “Come, O Thou King of Kings” (Parley P Pratt, Hymns, #59) still has the “heathen” : “While all the chosen race / Their Lord and Savior own, / The heathen nations bow the knee, / And ev’ry tongue sounds praise to thee.” (See T&S and BCC for commentary.)
Using General Conference as proxy, the frequency of Mormon usage of “heathen” diverged from that of the mainstream in the latter third of the 1800s but by the early 1900s it was declining towards secular levels (see graph).
The graph shows instances per million words, smoothed with a five year running average. That is, the plotted point in 1901 reflects the average of the frequencies from 1899 to 1903. Davies, Mark. (2010-) The Corpus of Historical American English: 400 million words, 1810-2009. Davies, Mark. (2011-) The Corpus of LDS General Conference Talks: 24 million words, 1851-2010.
 “when night came on we called to one house the man was a Methodist and began to talk with him he said he was no heathen and told us he had been told we come to Texas and called the people heathens here and said I want you to understand I am no heathens and if you want to Stay all night you can but I don’t want any of your doctrine in my house So I told him we would be glad to Stay all night he Said I will See the wife and went in and came back and told us to come in the house So we remained all night his name is Mr. Asbill.” (Clark, 1900 Nov 19 Mon);
“when night came on we ask for Lodgings he pretended he was Sanctified and holy we was treated good until morning when we Started talking on the Scripture and come to Baptism when we differed the lady said her man was as good as I was and her too and said why don’t you Stay at home and Preach to your People and not come here we are not heathens She was angry Because I had out done them on Baptism I have forgotten their names.” (Clark, 1901 Mar 08 Fri);
“we go to a house the man was at the gate we tell our Business he said we are not heathens here and walk in the house and leave us standing at the gate.” (Clark, 1901 Jul 25 Thu)
 “cold norther. we leave mr Stoveall and go to Canvassing go nearly all day without any dinner or Supper … we go over to the School house and fill our appointment there was 10 or 12 people came out … after meeting the good heathens left us in the School house … (Clark, 1901 Mar 20 Wed);
“At 4 p.m. we called on a Mr. Miller who had entertained the elders last spring several times. … I thought they would be glad to see us but they had turned heathen again. She said she didn’t think they could keep us as they did not have beds enough without making one on the floor and she thought that too much bother. I thanked her and we walked on….” (Jones, 1901 Nov 21 Thu)