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?
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.