I think there are bits of a lot of different political philosophy that work just fine on their own, and there are bits that jerks and zealots can over emphasize to polarize and exploit people that want to belong to a given movement.
Because I don't want to demonize anyone that may feel that 75% of a philosophy is close enough to associate themselves with it, in broad terms, for example, I'm just going to throw this out there.
No matter how stringently you may want to interpret it, mandating vaccines for deadly and/or chronic diseases would seem to easily fall within "providing for the general welfare" and "providing for the common defense" of the country.
Not all threats to the population have to be people from other countries that want to kill us with weapons. In fact, given that some weapons are actually biological agents that may be deadly and/or chronic diseases, this would seem to be all the more evident.
I guess what I'm saying is, if you want to argue for more or less government intervention, this probably isn't the hill you want to die on.