I think the Church has a say in some things because is followers comprise a constituency (as in "a group of people with shared interests or political opinions"). They represent cultural traditions that don't really stem from a deity, even for many of those of that faith.

They don't have to explain the supernatural part even if they think that it is the only basis for their view. They may have to explain their position though, in the same way as anyone else.

So, for example, in the House of Lords a bishop's experience and viewpoint may be no less useful that some of the others there.