Of course they do. It's impossible to know whether or not God exists based on physical evidence; that's why religion is based on faith and not scientific research. People choose their religious beliefs, or (much more commonly) have them chosen for them. That's faith.

You make your best guess about whether God exists. You don't choose if it's true.

Also, faith means "trust", not "irrational opinion".

> faith means "trust", not "irrational opinion".

Not quite, faith means "trust" in an "irrational opinion". Howerver, everyone should have the right to trust whatever opinion rational or irrational.

If you want to be precise, it means "trust in a person" in the original Greek. As in, the New England Patriots have faith in Bill Belichick.

That sort of faith can absolutely be rational.

Exactly why you can't discriminate based upon religion.

Of course people do. That's why there are many religions with many different gods.

Sure they do; it's all in their head.