Yes.
Certain specific religious groups go on anti-choice crusades.
Say. Their. Names.
Yes - only certain specific religious groups (i.e. the ones that make up most of humanity's religious adherents) are anti-choice. In the same sense, only certain specific cars (i.e. the ones with internal combustion engines) are responsible for most of the transportation-related greenhouse gas emissions.
Painting "religion" with a broad brush makes needless enemies. And we do not need to be doing that on an issue as important as fundamental human rights for women. Stop it.
It isn't me doing this. We lump "religion" together in all sorts of ways.
We give special tax breaks to groups if they qualify as "religious" that they wouldn't qualify for otherwise. We give special regard to religious matters of conscience that we deny to people with deeply-held non-religious beliefs.
Unless we want different standards of treatment for religions favoured by the government and religions out of favour (which I hope you agree would be a horrible idea), then our policies are going to treat "religion" as a broad brush.