As an American Christian who was a Republican as a stupid teenager, I will confirm that your description of Christianity (social justice, compassion and peace) is correct. There are a couple of factors that lead to it being the cudgel they’ve chosen:

• In the early 20th century, there was a fringe Christian belief called “dispensationalism” that gained power because southerners who had been solidly defeated in the Civil War thought that their defeat and the subsequent emergence of some tiny modicum of civil rights for Black people represented the end times; and the very faithful in the South pivoted from avoiding politics into being active in politics.

• In the 1970s and 1980s, a group of Republicans realized that they could use the Christian base in America to gain more power; so they created the myth of a “Christian nation” and set up Ronald Reagan as the “Christian candidate” against Jimmy Carter (who actually was a Christian, ironically).

• Republicans, as nominal conservatives, are trying to capitalize on an illusion of “restoring a lost America”—one which never existed in reality, but which has a strong nostalgia factor as a result of its presence in movies and TV shows set in the 1950s. It’s very enticing for baby boomers, who were very young during that time and thus have rose-colored glasses for it. This illusion includes Christianity as a cornerstone.

In short, Republicans warped the religion into something they could use to exert power. Something that evil people have been doing for 2,000 years (see also: the crusades).

If you’re interested in further reading about the topic, I recommend Jesus and John Wayne by Kristin Kobes Du Mez.