But some of them are doing exactly that: https://www.nytimes.com/2019/06/23/world/europe/abortion-men...
Furthermore, more than 50% of pro-life folk identify religion as their greatest source of guidance for deciding right from wrong (compare with less than 20% for pro-choice folk). [1]
So yes, most pro-lifers are driven by their religious beliefs.
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[1] https://www.pewresearch.org/religion/religious-landscape-stu...
I'm all for freedom of religion but I personally would rather not have laws that apply to everyone be based on the religious beliefs of a portion of the population which it seems like a good portion of religious people are trying to do.
Separation of church and state please.
Abortion epitomizes a hard moral problem, and frankly I doubt we'll ever be able to solve moral quandaries the way we can solve differential equations. However, I have zero desire in having the solutions legislated based on some group's religious beliefs.
Of course, one could argue that pro-choice folk are equally susceptible to dogma, but it's not as though they're forcing pro-life folk to have abortions.