I’d say the shift began with Reagan and his alignment with fundamentalists, and continues to this day. It was a good tactic in the early stages of forming an alliance between social conservatives and the GOP. But obviously now, since the GOP decided to try and take the only momentum which existed in 2008 which was Ron Paul and his Tea Parties and form them into a new moral majority they discovered that the old voters were dying out (literally) and that running on social conservatism and “values” no longer works as it did before. The beast which they created is now attacking the master, and it’s pretty fun to watch them devour themselves.
However they still try to placate the Fundamentalist Christians and social conservatives by their VP choices. Palin and Ryan were both attempts to appeal to the old moral majority voters which were started when Reagan and the GOP allied themselves with Fallwell and other fundamentalists. George Bush I was a natural progression from Reagan, and George Bush II was also quite appealing to the social conservative “base”. Id say if Christie does get the nomination that they’ll have to take a hard turn to the right during the election and get someone like Cruz on the ticket so the Moral Majority doesn’t decide to stay at home.
So they’re just influential enough to be placated, whereas the democrats have nothing similar or don’t even care much about their base. They know they’ll generally turn up to vote against the Republican so you can forget about Clinton allying herself with someone like Warren. She just needs to stay moderate (Center left) and get someone boring like Al Gore and she’ll be a shoe in.