If government has the right to decide what is “the best interests of the child” and NOT the Parents, then Government Can and WILL outlaw Bris Milah!
The government already can outlaw circumcision if it wants to, so long as it is not specifically targeting religious practice. If it bans circumcision for everybody, and its motive is not to attack religion, then it has the power to do so.
It can make an exception for religious purposes, and if such a hypothetical ban were to pass it almost certainly would make such an exception, but it would not have to. It would be entirely within its powers to say no exceptions, and we’d have to go to another city or state for milah, or do it illegally.
Nothing we do or say about vaccines can change or affect this. Governments inherently have this power. The reason they don’t ban milah is not because they can’t but because they don’t want to.