This is mostly a pointer to DOL's Tim Shaughnessy's post, where he makes the anti-abortion case for libertarianism (and more to his point, the case for religion). I think this is an interesting topic for libertarians to think about precisely because they do seem to come off overwhelmingly in favor of abortion, and it is the party's official platform. I don't have a firm stance on the issue simply because I can't decide, I seem to agree with whoever is arguing their point at the moment (assuming it is a good point).
I tend to think that the role of government is to offset coercion. Yes, the government makes would-be murderer's worse off when they are denied or discouraged from killing someone else, but that merely offsetts the coercion they were to place on the person who was going to be murdered. To me, it is not clear there is or is not coercion because of the ambiguity in determining the human status of the fetus.
My understanding of the Supreme Court's Roe v. Wade decision was that since pregnancy is a medical condition, and the government has no place knowing what your medical condition is, they cannot punish those who terminate their pregnancy. I get that, and that kind of wording seems on the surface a fairly libertarian take (welcome to disagree). However, the government's knowledge of the existence of a person does not seem to grant others the right to murder them.
Ultimately, I think that libertarian philosophy brings nothing new to the abortion debate and we should justs accept this. If the fetus is a person, then the government has a police role to play. If they are not a person then it's not the business of government to intervene. I think this is a improvement over an entire political party taking a stance on it, which mostly seems to serve as a bundling strategy for political views.
Disagree if you wish. Insightful comments that are respectful to everyone's views are welcome.