They cannot force it, not even the government can force you to get a vaccine.

But they almost certainly can (and likely will for some period of time) exercise their right to refuse service to anyone, including those who don't get vaccinated against what our dear leaders have convinced everybody is catastrophic threat.

Over time it won't be necessary, enough people will get the vaccine that it will won't be any more of a threat than other relatively rare communicable diseases like TB.