I don’t think it’s rooted in racism, I think the broad bible thumping culture is rooted in all the revivalism in the United States (we’ve had a few waves of it), and probably up until the 70s it was broadly black and white and not strictly political. The rise of Falwell’s Moral Majority and actively involved political religious fundamentalists came from Roe v. Wade I think first and foremost, and then greater acceptance first of gay toleration (in the 80s) and later outright gay rights. I think the large number of black evangelicals held similar views on abortion and gay rights at this time, but the Republican party itself had become so antithetical to blacks that there was no real way they were going to join the “political” religious right because that would’ve meant abandoning the Democratic party that they had switched allegiance to in the 60s/70s as its stance on Civil Rights changed and its stance on things like social welfare appealed to the black community.
I think in the pre-political days, white evangelicals, disproportionately concentrated in the South and often associated with lower education levels were probably racist to a higher than normal degree. So I think once you had a clear “politicization” of the evangelicals it shouldn’t be too surprising this base of people from which RR arose brought with it inherent racism.
So I guess I don’t think RR as a political movement evolved out of racism. I think it evolved out of evangelicalism, which included both black and white churches, but only the white churches got on board with the Falwell brand of RR, which caused a “racial political split” that didn’t necessarily exist before. I think this split has probably heightened the sense among RRers that blacks are “the other” and possibly made race relations worse, and I think given the demographics of white evangelicals a lot of them have always been racists.