For many religions, this just isn’t true.
I can only speak for Christianity, but the “reason” in it was only for the sake of supporting or propping up their belief. They would only permit “reason, logic, evidence, facts” if it helped them, and methodically discard everything against.
Said another way, reason is the emergency patch they’re sticking onto their increasingly leaky boat. They desperately want to get back to “Don’t think; we’ll do all that for you.”
It is when someone with The Book wants something from you. When their actions depend on belief and that belief does not sway you. It’s at that moment they say, “God wants this because…” and then fills in the rest with whatever reason they’ve cooked up.
I don’t mean to imply they use reason as we understand the term. The Holy Purpose happens to be the same as anyone who tells you about it.
Religions historically have tried to use facts and reason to support them, but as they were proven wrong again and again and again retreated from that. Attempts to support religion with reason are fundamentally hampered by the fact that they are both wrong and irrational, to the point that it’s predictive; if a religion claims something you can pretty much just assume that it’s wrong. If it wasn’t wrong, it wouldn’t be claimed by a religion in the first place.
Because of this religion has largely collectively given up on reason and facts, and relies on faith, lies and coercion to promote itself.
Many of the amateur scientists from the late 18th and early 19th centuries were clergymen with time on their hands, who studied the earth to try to prove the Bible true. They wound up proving it false, but most of them were honest enough to admit it. Many of the religious could handle the earth being older than the Bible said, but Darwin showing we were not specially created was too much for them, and the fundamentalists turned their back on science, as they have to this day.