There are many different types of proof. Usually when someone asks for proof of something, they mean that they don’t believe you because either they think you are dishonest, irrational, or both.
I cannot prove to anyone whether proof is relevant or irrelevant, but I see it as irrelevant most of the time. I have nothing to prove by doing this but I can give you some proof of how I came to this idea.
Geometry nerds sometimes try to prove that two triangles are congruent (identical or same) in every way. I love triangles but I don’t bother with this because I am not racist for or against polygons.
There will always be those people who try to prove that “cats are liquid”, “pi is irrational”, “the earth is flat”, or that “video games are satanic”. I don’t let these people bother me so much. No amount of proof will stop people from promoting ideas when they have a motive for doing so. The motive, whatever it may be is more relevant than the relevance of the actual subject. I can learn about people by listening to their proof.
I have my own thoughts and opinions and that is enough for me. In no way am I affected by someone else believing that the earth is 6000 years old. I only need to know that it began sometime before May 15, 1987.