I have owned businesses. 3 to be exact. Built them from the ground up and sold them. I also currently manage people.
Yes you can set policies and guidelines, but they need to adhere to laws. So no, business don’t have the right to do what they want or pound sand find another job. Certain things you cannot do and certain conducts can get you in serious legal trouble.
Lots of jobs require various vaccinations. That’s nothing new.