Framing this as "privacy" makes no sense.
Framing it as "choice" can be coherent if you express it this well, but most people don't.
(I think I weakened my own argument here by including that sentence, but too late to edit it now. What I was trying to express is that this isn't actually a sexism thing: I have no trouble imagining these people applying the same standard to men in a world where any human could get pregnant.)
Both the draft (or any form of compulsory service) and taxes are counter-examples.
You're probably going to object to taxes, but it's reasonably well established that wealth is health. (It's also true that taxes are spent on things that don't save or preserve the life of another human.) More to the point, taxes take my time, which I can't possibly get back.
Interesting enough, so does prison.