Public schools in many (most? all?) municipalities require kids be vaccinated against several things before being allowed to attend school. This has been the case since well before I was born. This is a government setting the requirement. Now, perhaps it is not legal for the federal government to set this sort of requirement. But maybe it is.

Which is state-mandated, not federal, and done by passed law, not by executive order IIUC. That's still a huge difference.