The 'well we have mandatory things already, so why not this also?' is what you are using to argue against the vaccine. I think a little nuanced thinking goes a long way when comparing all of the examples you proposed.
Please note I am not arguing against the vaccine. I am fully vaccinated. I am against limiting parts of society to people that haven't been vaccinated no matter the reason why. There is a big difference (I have all my vaccines, my son also has all his vaccines, and he may or may not get the covid vaccine depending on the recommendations for his age group).