So your two examples of the drunk driver and vaccines are different. You don’t have the right to drive or go to school. You are granted that privilege by the government. Part of those privileges involve consent to certain requirements. So in those cases, the government is simply forcing you to uphold the agreement put in place. If you used this reasoning to support your argument, it would be like saying bodily autonomy is a privilege granted by the government. Maybe if you’re at a breeding age they would prevent you from sterilization (so you can procreate for the greater good). They could tell you not to get a tattoo (or go full Hitler and force you to get a tattoo).
You say you would not be OK with the law, but would comply. How far does that go? Would you support another military draft? Potentially being put into deadly situations (especially if you don’t agree with the war/whatever is happening)? Forced labor if it was for “the good of the country” or some reason (maybe making a product you don’t agree with e.g. drugs, guns, late term abortion kits)?
If someone were to refuse to comply with any of these laws, what should the punishment be?
Edit: What if the government tried to mandate forced abortions? If they can declare something necessary “for the greater good”?