The main issue is that the Republican party has tied themselves to single issue voters and the kind of religious people who support a ban. They need those voting blocks to keep getting elected.

For a single issue voter their pet issue is the only thing that matters. They will vote based on that one issue alone. There are a few issues like that but anti-abortion is a big one. If the Republican party dropped it they stand to loose a lot of votes and thus elections. No, they wouldn't necessarily attract a lot of pro-choice people. Maybe a few if the person is mostly conservative but was pro-choice.

The reasons someone would actually support a ban on it basically comes down to how they view it as morally wrong. Almost always it is based on the person's religious views.