from what i hear, applying to residency is more about a good fit than getting into the highest ranked program you possibly can. if you wouldn't like the #1 program and they wouldn't like you, then the already miserable experience of residency would be even worse.
so the way i see it, if your politics/beliefs in choice and reproductive freedom are important to you, why would you want to be in a program that is against that? your political and ethical disagreements would be bound to come up if they felt strongly and you did too, so i would think it would be better to have a program like that crossed off your list sooner rather than later. this seems like it would be especially true if you are going into ob/gyn since the issue would be more immediately relavent.
i can see this being an issue for med school admissions, but it seems like the differences in the residency application process might make it less of a big deal. but this could be naive. i'm not really sure.
being a member of med students for choice and having that on your CV does not seem to hurt people for residency.