Well, the most conservative I think the US could realistically get would be a country where abortion is extremely limited in nearly every state, gay marriage is illegal, immigration is severely restricted and in general culture is much more conservative. I would really hate living in this world lol, but here's a half baked timeline.
1.) The Second Great Awakening happens differently, between 1850 and 1920 American faiths develop differently. No specific PODs, but a few speakers are different, a few more influential books are written in a certain direction, and all this results in a less racist and more universalist kind of faith, with a greater focus on charity. Also, more churches end up as OTL Mormons, in that they are generally more cultish. This wouldn't be all churches, but enough of a general trend.
2.) The wave of immigration wave of Europeans between 1880 and 1930 is significantly less than OTL, maybe only 10% of OTL's numbers arrive. This is because of greater pressure on the government to limit immigration in the north.
3.) This slows down American growth and expansion massively, e.g many territories will become a state a decade later than OTL, or the Dakotas may become a single state ITTL. This lack of growth from immigration is somewhat counteracted by a larger natural growth, as these religious changes tend to promote larger families. Importantly, it keeps the US more rural than IOTL.
4.) Northern recruiters go south for their factories since they can't go to Europe. This results in the Great Migration being even larger, and a much larger African American population in the North and West. For example IOTL in California in 1945 African-Americans were 1% of the population, while ITTL they would be 20%, while in New York around 1/3rd of residents would be Black for example.
5.) This leads to earlier education and economic growth for the black community, earlier representation in Congress.
6.) TV becomes commonplace in the 1930s instead of the 1950s, so segreation ends 20 years earlier.
7.) Culture becomes more progressive between the end of segreation and 2020.
8.) By 2020, the US is dominated by rural and religious voters due to little immigration. Religious sects nationwide, mostly rural, have high birthrates comparable to OTL Mormons, while cities have little growth due to little immigration, and much of their growth in the 21st century has come from these religious minorities sending their excess kids to the cities. This means that in urban areas parties still have to toe the line in socially progressive politics. However, with less immigration the labour rights movement grows even stronger in the early 1900s. Also, importantly this America develops as a bi-cultural approach, where the country is seen as a mixed African-American and Anglo-Celtic one, just as New Zealand is seen as a mixed Maori and European country by it's residents. A more similar culture and a small population, combined with churches preaching more compassionate government policy enables universal healthcare nationwide in the 1960s, and greater worker's rights. However, 'traditional family values' are also pushed by law. Unfortunately by 2020 only Maine has gay marriage, 15 years before OTL, with 3 other states having civil partnership. In urban areas women's rights are similar to OTL, but with only 60% of the US being urban this means in the rural areas the idea of 'mother first, life second' is still sadly pushed onto a lot of mothers.
Good enough for you? Not very realistic and bad for LGBT folks (myself included), but if nothing else this USA would be less racist and have more healthcare protection.
