The recent vote in Ohio is just one of a string of cases where voters show they mostly support abortion access to some extent (1). Polls show the same. (2) So why do Republicans (specifically Republican politicians, not necessarily Republican voters) keep trying to do something unpopular?
My (perhaps cynical) view of Republican politicians is that they’re the “do anything to win” party. They would take any stance and pull any trick if it would give them a better chance of winning. So why are they so stuck on a losing issue?
Even then, it still doesn’t make sense to push so hard for restricting abortion. The extreme righters will vote Republican regardless, and they run the risk of alienating the center/undecided voters. The vote margins when they win were already super thin as it was…
It’s a question of which side will see more voters activated by the issue, and go on to vote: remember that winning is largely about generating the momentum for people who already support you to vote at all, not just swaying hearts and minds to vote for you. It’s barely that latter at all.
So they calculate they can get more church ladies and reactionary males to get fired up about protecting babies and punishing jezebels than the democrats can get people fired up about protecting women’s healthcare. Given how shafted women are across the board, betting on hate may be a winning move.
Republicans (conservatives, generally) have limited empathy. Relatively few people will ever have the need to seek an abortion as a percentage of the population - only half are even eligible. The lack of empathy means they do not consider that it is a problem for them until it actually happens to them. For the base it’s a litmus test which allows the candidate to do or say almost anything and still guarantee a vote; for the rest who have never had to seek or don’t expect to need to seek an abortion, it’s a non-issue and they can cite more (American) moderate right policies like lower taxes and less regulation as their driving force.