A lot of places and venues around the world have already adopted the policy of no vaccination, no service. I wouldn't want to sit and eat next to someone who choose not to vaccinate themselves in a pandemic not because they cannot, but because they are stupid enough to believe in lies and misinformation. It's all about health and safety, nothing about discrimination, politics or whatever. If there was widespread measles, would you go near someone who choose not to take the measles vaccine?
Vaccination should be like wearing masks. Either you wear one and go out or you stay home. To put other people's lives at risk because of your stupidity is being irresponsible. There is no discrimination when health and safety is involved.
Mandatory vaccination is already in force in many countries and is the way to move forward. Either make it mandatory by law or deny antivaxxers healthcare subsidies should they fall ill because of COVID. It's a fair call.