IMO this should not be a federal issue. Each state or school district can set their own rules (thus provide the option to parents).

This would pretty much make everyone happy. As most regions would setup the rules to best protect their children.

Now, I'll point out this is effectively is already a thing. You cannot attend school in many locations without getting your vaccines and / or providing a valid reason why you needn't have them. This is the beauty of living in a system which supports state rights. Similar to how Italy and France can set their own laws, so can the states in the U.S..