Yes, if it's a health issue, as we've seen in Australia, then "forcing" one to cover their head and hair is completely OK. No one complains that the supervisory powers are bullies, or are demeaning to the staff. And it can be a federal policy.
So what is the problem with people not wanting Muslim women and Sikh men doctors and other professional physicians to cover their head and/or hair again?
"St. Francis Hospital In Hartford Is On Probation For One Year -- Courant.com"
"The investigation report also cited several problems with hospital facilities.
. . .
"Meanwhile, the report said, numerous staff members in operating suites were wearing head coverings that failed to completely cover their hair, even while they were directly over or within direct contact of the surgical sites."
Yes, I did notice that it says "operating suites". Which is kinda funny, because if hair is not a good thing during surgery, then how is it OK during any other procedure? Wouldn't it be wise to allow head and hair coverings in other suites as well? Of course, I've not studied medicine.