Doesn't this description fit to every religion? It isn't like any of those are founded on rationality or empiric observations.

I think it's fair to say that religions spawned from an explicit desire to negate a particular aspect of the Catholic Church indeed is devoid of that particular aspect. That doesn't mean that protestantism is entirely rational, it's still a religion; but it's by definition different from catholicism in those specific ways that led to the schism. For example, I friend of mine got kicked in the butt publicly as a child by a priest because she dared to say that the host "represents" the body of Christ (while, clearly, it literally is the body of Christ, not merely represents it)

Some protestant denominations believe the host is the body of Christ, others that it only represent the body of Christ.

There are lots of religions, and lots of sects of religions, with wildly varying claims, methods and cosmologies… some of which are true, some of which are not, and possibly in ill-fitting overlap, some of which that are rational or more rational, and some of which are irrational or less rational. It would be incautious to label them all irrational while only truly considering a small number.

As opposed to putting a little box on your head and going to a wall?