Well no one's going to say "I oppose women's rights" because that's not (yet) popular enough, although we are headed in that direction. I'm not a big fan of the "argumentum ad hominem" on this issue, but the idea that restricting women's rights isn't anti-female just because the people advocating it don't sell themselves that way is rather silly. People who opposed women's suffrage had nominally pro-woman arguments, as well.
The thing is, pro-life activists would resist conceiving it as a women's rights issue at all. By your logic, a hypothetical proponent of allowing women to commit murder would be pro-woman, and anyone who wanted to punish woman murderers would be anti-woman. This hypothetical sounds preposterous, but this is what it sounds like to people who are pro-life.
Of course, acknowledging it as a women's rights issue doesn't mean that pro-lifers have to become pro-choice. As your example shows, there are valid limitations to "rights". Nonetheless, pro-lifers do want to restrict women's rights, so if you don't see abortion as murder, that becomes the deciding factor.
You're claim requires a bizarre definition of 'rights'. No one is going around calling the laws against violent crime restrictions on the right to bodily autonomy. The question as always, is whether unborn babies are persons.
-Exactly. I firmly stand on the non-person side of the fence, of course. Thus, I obviously do not see abortion as murder. However, given that reproductive rights are a matter of the future of a people, and are, therefore, a vital matter of interest to the state, I see total liberty in matters relating to reproduction as risking the degeneration of future people, and I am thus perfectly willing to examine arguments for abortion restriction.