No, you don't have to be religious to understand what religious symbols are about.

You can understand them, but there is no point for you, since they don't mean anything to you.

Depends on how much "supporting evidence" you give me.

I don't really think I got your point. All "evidence" that the bones in location X are really those of St. Y, won't have any effect on you, when you don't care about St. Y at all, because you don't believe in that religion.

Imagine you have no religion, but are feeling spiritual and want to find something real. Do you go to the church of a religion that claims it has the actual remains of their saints, or the one that only has pictures and empty walls?

Actually, maybe that's a stupid question as people absolutely do both. But there is an element of "look how great we are because we have a splinter from the holy cross in our church".