Something like that is already happening with people who refuse to wear masks. In Texas, where their governor killed the state mask mandate, he said businesses can keep on enforcing their own rules. People are getting arrested for trespassing when they refuse to mask up or leave in stores that require it. Once enough people get their immunizations, I suspect we will get "immune passports" that let you go without a mask (if you are dumb enough to do that!) Then I bet it's going to get really limiting to refuse masks and vaccination. It will be volunteering to be a second-class citizen. Like having to find a "Colored" bathroom in the old South.
