I think it's the opposite, really, if you're talking about the direction of change. The GOP has become increasingly hostile to Christian beliefs, while Democrats have become increasingly accepting. Even 20 years ago, I think it would have been impossible for the Christian right to embrace a man like Trump. Different starting points, though.
Probably generally true that anyone jumping forward 30-50 years in time without changing any positions would have trouble in a presidential party. See above on Trump. One reason I think the recent trend in some corners of digging up old opinions and then declaring politicians unacceptable to be really dumb.
I'm sorry, but this seems both A) really silly, and B) completely unrelated to presidential elections. Like, it's hard for me to address the point because I don't see the issues as even being worthy of attention. How many boys in the country have participated in girls schools? Three? Four? 10? Whatever harm one thinks came to the girls who had to try to kick a soccer ball past a male goalie really pales in comparison to the harm done by the GOP restricting access to healthcare for millions of people or pushing to allow more pollution.