Excellent observations, thanks. If I could add just a bit, another way the Republican/White Evangelical movement maintains disproportionate power is through political tricks like gerrymandering, which is increasingly becoming an existential crisis for our democracy. Ohio is a case in point, where the people as a whole voted solidly against Trump but where gerrymandering put Republicans in something like 80% control of the state legislature. Evangelicals don’t have any larger share of the population in Ohio than anywhere else, but extremist gerrymandering has given them an absolute lock on political power, grossly disproportionate to their voter numbers.
My other point is less important, but I feel I should add it the sake of accuracy. Very few white Evangelicals oppose contraception. They do oppose medication that they consider abortion inducing, even when doctors say that’s not what it is. But that isn’t some sort of backslide into actually opposing contraception. White evangelicals, from my personal experience as the son of a Baptist minister, enthusiastically embrace almost all common forms of artificial contraception.
Evangelicals often ally with conservative Roman Catholic political groups, and since those groups often strongly oppose contraception, it’s possible to see hybrid organizations sending anti-contraception messages, but it’s not an Evangelical priority.