I suspect far more people would be libertarians if they actually thought through the possibility of the statist measures they support being put to use by their opponents. Coyote Blog points out an interesting incongruity. The National Organization for Women is adamantly pro-choice, and vehemently opposes any attempt to have the government restrict a woman’s right to have an abortion. This is usually phrased in libertarian terms- it’s wrong for the government to deny a woman control over her own life and body.
But NOW also supports universal government-provided health care. In other words, NOW (and I would imagine most pro-choicers who aren’t libertarians), wants to create a system where the government will have massively increased incentives and justifications for controlling private decisions affecting health- what people do with their own bodies, in other words.
Now, in purely philosophical terms, there’s no contradiction, slogans like “A woman’s body, a woman’s choice” notwithstanding. Feminists, being predominantly liberal/leftist, generally don’t derive the right to abortion from some broader right to control your life and body in general, a few libertarian feminists excepted. On the contrary, abortion is a rare exception to the general rule that the individual doesn’t have any right to control those things.
It does, however, strike me as a potential strategic risk for feminists, and for anyone else who doesn't want the government controlling women's reproductive choices. If we had a Canadian-style system, where the government not only provides health care but outlaws private alternatives, it would be a quite simple matter to make abortion de facto restricted or illegal. Don’t outlaw abortion- simply make all health procedures a government monopoly, and then refuse to fund abortion in some or all cases. This would, I suspect, be quite popular, at least for more controversial areas like late-term abortions or abortions for minors. Such a result would be appalling to members of NOW, but it would hardly be the first time liberals found themselves unhappy when someone else managed to seize control of the oppressive state machinery the liberals built.