I feel like this isn't at all what most religious people are doing and that you're presenting some kind of strawman to make them seem alien and dumb
There's really roughly two camps, one which is very much questioning the existence of God and are actually busy trying to find the answer to the existence question by finding evidence. Sometimes in scripture, sometimes in others or in nature. Often these people are actually somewhat open to counter arguments. These people are generally somewhat equivalent of physicists with a pet theory they're trying to pursue, develop and prove, say string theorists.
The other camp believes strongly, and isn't so much involved with whether or not God exists, but instead they deal with the details. They might think about how the trinity works, talk about trying to reach the youth, working on helping people in their local community, etc. These people are kind of the equivalent of physicists who work within the existing framework of established physics. Whether that's through applied physics or by say trying to analyze the composition of some star.
Granted, this might be a cultural thing and there a cultures where the beliefs are less practical and more intense, including intense studies of holy books. But most people around me that are religious don't do that. It's just been my experience.
There are many ways of understanding the world; rational thinking is only one of them. Note however, that the kind of theology that organized religion is usually known for is a kind of, perhaps misguided, rational thinking. The real core of religious thought is closer to direct theophany.
(Note that a genuinely rational account of theophany and such is quite possible, but only at a meta level. The way you directly engage with such things is what leads to the distinction I'm referencing here.)
I don't know anything about religious thought. Not that it doesn't exist, but I don't know anything about it. Like I said, the way I see it, most people find value in it for practical everyday life. And the older I got, the more I understood it -- life is definitely easier if you are convinced of something and don't question it. But in that view it's mostly for the earthly things, and less for the religious thought.
The sciences have the experimental part, which is a method made possible by the kind of phenomena you observe. As far as religion is concerned, I don't want to oversimplify, as I think we run the risk of lumping everything together, as there are different interpretations as to what a religion is.