This goes back a long way. Many of the early American colonies were founded by religious extremist sects being pushed out of wherever they came from. The US and UK both experienced the First Great Awakening, but the Second Great Awakening was unique to the US. This led to entirely new sects like the Adventists and Latter Day Saints. It led to an extreme backlash against Enlightenment ideals. Post-millenialism spread rapidly and many Americans were convinced the return of Christ was imminent and American society needed to be purified, which resulted in the first tight intermingling of religion with politics. Religious organizations needed political clout to accomplish their social goals, which were not restricted to their own followers. This was heightened all the more by the reality that the outlying territories didn't have real governments and religious leaders were the only leaders around. Revivalism mixed with frontier folk libertarianism to produce what would eventually become prosperity gospel teaching that the strength of one's adherence to strict behavior and love of Christ would lead to material success, and thus the rich must be pious. The Third Great Awakening gave us American Christian organizations that became increasingly all about social reform in light of the belief that Christ's return was imminent, leading to the very earliest alliance of the Republican party with activist Christians, which was the effort to abolish slavery. That alliance eventually dovetailed quite nicely with the American GOP's post-New Deal long game to cut taxes, business regulation, and social welfare spending, thanks to those earlier seeds of prosperity gospel. This also explains the largely unique to the US "god and guns" phenomenon, which is more about identity politics than religious doctrine because revivalism was tied so tightly to the frontier, where personal firearms ownership and proficiency was all but mandatory.

All in all, I think you get a nice picture of how something well-intended can end up in a bad place. The righteous fervor to make society better resulted in ending slavery, fighting against tenements, but then they ran out of the most obvious evils and we got prohibition, anti-homosexual laws, and this mobilization of single-issue voters that judge all office holders solely by whether they'll try to abolish abortion and don't care about anything else they do. Tack that onto the naked charlatanism of prosperity gospel and you more or less get everything wrong with 20th-century American evangelicalism.