No it isnt, but the fact this is already on the table and out there won't prevent this from going even further and taking the next step.
Misidentification in the medical field is, as a default, something you can't do in any other situation. If someone gives a name of Steve and provider decides Steve looks like a Joe and calls him, you can't do that and not face consequences.
And when you are in the medical field it is NOT about you and your personal whatever the hell it is when you are working with patients. It's unprofessional, rude as hell, and grounds for discipline in any other situation. They don't really have any grounds to stand on with their claims religion anyways, so, yeah, they can bugger off. It's not about them.
And because misidentification is grounds for malpractice, and a big cause of medical mistakes, there's also legal grounds covering this.
But these selfish Christian snowflakes and other RWers want to cry and whine and demand special privileges to be exempt from the law and only for very specific circumstances (that they cannot justify using their religion).