This is different than just asking., They are REQUIRING it.
It’s not required. Work is a voluntary relationship. They can always quit.
There’s nothing terribly new about any of this. Surprised people are acting like it is. Try to go to any school and not show proof you’re up on your MMR. You can’t. Most medical employers make their employees get the current flu vax. This has all been well established before. The employer is within their rights to make the request, and if the employee doesn’t like it they are free to go elsewhere.