You felt compelled to speak out in their defense, but your choice of comparisons and rhetoric is precisely why I felt compelled to clarify as well and what made me raise an eyebrow on the logic in it. That is to say I think you chose your example, and to make it in a intentionally hyperbolic way with things like "banned from civil society" and "horrific, dystopian, nasty, bullying" because you saw that it would make the most emotional impact to compare to your acquaintances' situation, but that's precisely where I felt it was becoming absurd.
Having just now re-confirmed that levels of nasal virus drop faster in vaccinated people to make sure I'm not being illogical, the creation of laws that allow businesses, schools, and others to legally stop you from entering isn't "horrific, dystopian, nasty, bullying" the way you characterize it at all, like banning obese people due to their burden on healthcare costs would be.
To me, it really does come off as a trying to point out the issues with mandates by drawing it to the absurd conclusion of excluding overweight people from society. So hopefully that clears up why I saw it that way, but maybe I'm incorrect definitionally.
There are always going to be mandates or policies that conflict with what parents, or people in general want to do. To me that doesn't make it nasty or bullying, though they may feel horribly bullied if it affects them. If anything I'd say those feelings (and most examples of nasty bullying I've seen) extend from the acts of anti-science politicization of masks and vaccines, which in my opinion is a great disservice to the public. We now people who now feel like nasty bullies are creating new mandates in a nasty dystopian nightmare world, which I think is extremely unfortunate.