At the root of cancel culture is the freedom of association. Ultimately people either feel fraternity amongst each other or they don't.
I might argue that the freedom to not bake cakes or employ gay people with regards to religious rights is also part of the freedom of association. People either feel the love or they don't.
I might argue that the freedom to not bake cakes or employ gay people with regards to religious rights is also part of the freedom of association. People either feel the love or they don't.