To start off with, I should make clear that I'm not American, and will lack a lot of the educational background in US history Reddit will invariably assume I have: please be patient in that regard!
A question that has struck my mind recently is, how did religion work in the "Old West"? A lot of people were scattered across sometimes very long distances, and many of them would have been recent immigrants from many places across the world, especially Europe. Did frontier towns or settlements generally tend to the religious needs of the settlers, or was it accepted that the churches simply weren't out that far yet? Coming from NI I know first hand that Europe is the source of quite a lot of both denominations and conflicts within Christianity: how much friction was there between different religious groups? What religious denominations were the most common? What about religious minorities like Jews, or Chinese immigrants? How did religious demographics change over time, as settlements grew and populations of settlers increased? Lastly, did the creeping arrival of "civilisation" from the East make a difference in the religious lives of people in the west?
I appreciate that these are a lot of questions about a likely incredibly broad topic, so any insight you can provide is appreciated.
These are great questions. Perhaps it is no surprise that they are difficult to answer because generalizations are challenged by specifics.
The West is the largest region of North America (being roughly half the continent). This enormous region includes many very different environments that resulted in different economies and settlement patterns: Historians of the West are often inclined to speak/write about there being "many Wests."
In areas where there was sufficient water for farming, there was a tendency for people to settle in patterns of self-segregation, arranging themselves in locations that matched their own ethnicity and religion. There were always exceptions to this, but towns serving agricultural communities often had only one (or only two or so) churches that matches the nearby population. German or Scandinavian areas tended to build a Lutheran church, having settled near one another; places with more Irish, Italian or Polish settlers tended to build a Catholic church - and so on.
As a population would gain an inevitable diversity, there was often a Catholic church, a specific protestant church (Presbyterian, Lutheran, Episcopalian) and often a "generic protestant church, often reflecting American origins, that could serve as a "catch all" for all of the rest.
In the arid West, there was a tendency for more people to be clustered in cities, and because of the inevitable diversity, various religions needed to be present to serve the population. Again, there could be a reliance of a "generic" protestant church of some denomination that was flexible enough to serve diverse people. And there was typically a Catholic church for those who saw religion in more "specific" terms.
Often, ethnicity closed the door to access to that "generic" protestant church: African Americans typically worshiped separately, but because they were usually fewer in number in the West, congregations of the AME (African Methodist Episcopalian) church or the Baptist faith, often met in homes or in small rented or borrowed spaces.
A similar approach was often the case for Jews, who often held religious observances in homes, because there were too few to afford to build a temple. Larger Chinese communities often had a Joss House, which were misunderstood as serving in the capacity of a temple. The Joss house could and often did have that function, providing a space for religious observances, but it was also a place for administration of Chinese needs in relation to the old world government and these places were also centers of social and community gathering.
Much of the West was also settled by the Church of Jesus Christ of Latter-day Saints (i.e., the Mormons), and their congregations and structures were specific in a way that matched those of the Catholics, for example: the LDS was not a "generic" protestant church, and only Mormons were likely to attend religious services there.
I have seen primary sources talking about newly established communities welcoming a visiting minister, who was often received with excitement. Many of these residents were accustomed to attending to religious services, and in the first days of a boomtown's existence, many of its residents missed going to church. So when a preacher would visit and give a service or two, people often attended, even if the denomination wasn't exactly what they had known "back home." That sort of thing filled a need in the short term, but it did not take long for institutional churches and their ministers/priests to fill the vacuum caused by sudden settlement in remote places (especially in answer to a mining boom).
Friction between ethnic groups - sometimes based on religion and other times accentuated by religion - was common. Irish Catholics often resented Methodist Cornish supervisors in the mines, and violence between the two groups was common. This was based on religious differences as much as ethnic. Other groups were more likely to express antagonism more for ethnicity than religion, specifically, although hatred was usually inspired by the "whole package," so religion was often a factor.
I believe this approaches a path to answering your questions, but feel free to ask specific things!