Charles - you might want to revise your statement:

But why does it matter whether the procedure is invasive or not? The state has absolutely no business mandating any kind of medical procedure, and the very fact that this is even being considered is incredibly offensive.

The state mandates vaccinations, for public health purposes, and anti-vaxxers are more than willing and do use this kind of line of thought to claim that the government has no right to force the vaccination of children.

There are legitimate reasons to mandate certain medical procedures - vaccinations being one, blood tests for genetic disorders being another. But the procedures being considered here should be left to the doctor’s discretion in consultation with the patient.