I understand your anger and agree that anti-vaxxers are stupid. I believe public health education should be part of the school system.
I also agree that it's responsible for a society to impose reasonable restrictions on members that endanger it.
I think people do have an ethical obligation to take reasonable precautions avoid potentially exposing others to pathogens. Vaccination is an example of reasonable precaution. People have the right to bodily autonomy, do not vaccinate them against their wishes.
I do not support the firing of workers for refusing vaccinations if they can do their job remotely. People shouldn't have to decide between their religious beliefs and employment if their employment doesn't bring them into contact with others. (Imo anti-vaxx is essentially a religion, this may say more about my beliefs regarding religion than about anti-vaxx sentiment).
By all means exclude the unvaccinated from places where they can be reasonably understood to endanger the public, or others that have a similar right to be there.
Are you nitpicking an ally for using "exclusive" instead of "principal"?
Is that your point? That failing to acknowledge the nuance that sexuality exists on a spectrum must be addressed confrontationally because it's erasure?
Transphobia and homophobia are too often literally (yes, I mean literally) beaten into men. We have to work to unlearn it. If an ally says he wouldn't be able to keep it up if he learned the woman he was courting was assigned male at birth, believe him, but don't discount him as an ally. Imo your efforts are better spent combating active transphobia than policing your allies. If their terminology hurts you, suggest better ways to articulate their points but do it collaboratively instead of confrontationally.
Just my two cents.