Abortion is an issue that has deeply split the libertarian base precisely because it raises a lot of thorny issues. Libertarianism is about maximizing freedom of people as long as they do not infringe on the freedoms of another person. Is a fetus considered a person? This is a very complicated subject, and even a lot of pro-choice supporters are squeamish around things like late-term and partial-birth abortions.
No less a (controversial) feminist icon than Camille Paglia has stated that, despite her “pro-abortion stance”, she begrudgingly admits that the pro-lifers have the moral high ground on this particular subject. Abortion is really complicated, and I don’t think it should be surprising or morally repugnant when certain private sector actors bristle at having to provide or finance abortions by dint of law.