Not sure I would easily say that’s a slippery slope because veganism is different. Strictly speaking, one is not truly a vegan if they pay US tax because they are in fact contributing to animal exploitation. So vegans would be demanding a right to be vegan. Whereas your other examples don’t have a similar effect of denying someone to be who they want (the right to self determination in the declaration of human rights, IIRC). If someone tried to invent being opposed to public healthcare, they would be at odds with human rights to start with and would have to start with denying themselves public healthcare. These positions would be too extreme to defend, unlike defending one’s right to be vegan. Education is also a human right and they’re not overturning that easily.

EDIT: fwiw, I dug up the self-determination right I was fuzzy on, from the International Covenant on Economic, Social and Cultural Rights, Part I, Art.1:

1. All peoples have the right of self-determination. By virtue of that right they freely determine their political status and freely pursue their economic, social and cultural development.

That said, I’m not sure if that concretely allows a vegan to derive a right to be vegan. Perhaps it’s too abstract to be useful.