If the current anti-vax nonsense continues, very soon the non-vaccinated will be pretty much shunned from daily life. Debate about that is already ongoing.
I know for a fact that several countries are exploring this.
Without a "corona pass" proving that you are vaccinated (or exempt for valid reasons), you will not be allowed to enter restaurants, bars, festivals, shops, work places,....
Hospitals will not be part of that though. It would be very unethical to refuse health care to people who need it.
But the idea of "make life extremely difficult for the unvaccinated" is most definitely the next step in the vaccination campaign to get those stubborn people to come to their senses.
The step after that, if it still proves insufficient, is mandatory vaccination, like we have for plenty of other nasty diseases also.
Society shall not allow that a bunch of ignoramuses and conspiracy nutcases are going to prevent nations to return to pre-covid normalcy.