Compelling to do good things and compelling to prevent bad things are a duality. They're equivalent in their effects, and you can easily transform one to the other. Punishing people for doing wrong is compelling them to receive a punishment deemed good. "Thou must go to jail."
"Personal autonomy. Your body, your choice."
That's a nice slogan, but it isn't actually realized anywhere. It's always your choice when there's a clear advantage -- that is, when the state doesn't "know best" about your body. And it absolutely reserves the right control your body for the greater good.
"Can the state compel everyone to be a vegan unless they can show proof of a medical condition that would make it unworkable?"
They can if there is good evidence to show a vegan diet is strictly superior to all others.
So for a more appropriate example, it can compel you to use a seatbelt in an automobile, because there are real social costs to not doing so. It doesn't matter if you want to take a risk, once you go to the hospital, you are utilizing a public resource. And the state has a responsibility to ensure those resources are available and used efficiently, which means preventing unnecessary emergencies. (Like what would occur if you contracted something like polio.)