The strongest reason for libertarians to support women's voting rights is that it seems likely that voting rights are part of a bundle of expanded freedoms that women have acquired, which almost all libertarians support. These include all kinds of social freedoms, and, perhaps most importantly, property rights fully equal to those of men. It's difficult to imagine having all of the latter without the former.
Thiels response is in a vein sadly typical of libertarians, which is to see freedom solely as the the absence of certain government government policies. Pre-progressive era America was a less free place than America today, because half of the population has drastically more freedom, and because oppressive social norms have lessened their grip on society (much to the regret of conservatives, although not really- most modern conservatives implicitly approve of many of these changes).
Will is right (as usual)- if you accept that there's going to be a government- in part because people disagree deeply about the nature of a just society, then you have to accept the endogenous elements of that system. And even if you reject the legitimacy of government, you should applaud, not mourn, the recognitions of more human beings as autonomous individuals.
I do, however, want to partially agree with the sentiment of Arnold Kling's response to Will, although I think he's almost completely wrong (Will's response in the comments is right on). It seems pretty clear to me that violations of freedom are bad whether or not the violation is a the result of democratically decided policy. You don't need to reject the democratic system as such to reject the legitimacy of that policy (that seems to me, for example, to have been the position of Martin Luther King Jr.).
I do agree with Kling, however, that we ought to be open to alternatives to our current form of government. When we do this, we ought not to see democracy as holy- it's just a means to an end of a liberal society. But if we take the tentative position that what we've got is the best we're going to have in the foreseeable future, than lamenting the existence of democracy doesn't seem very useful.