Do Religious People Believe Religion?
You might think the title question is trivial; you might think that if a person does not believe the tenets of some religion then they are, by definition, non-religious. But let's make the question non-trivial. Let's count as "religious" any person who would sincerely self-describe as a Christian, a Muslim, a Jew, or a member of some other recognized religion. It is open to discussion whether these people typically believe the propositions that are usually described as the major tenets of that religion, or whether they identify with the religion for some other reason.
I'm not interested in caviling about small (or even medium-sized) points -- I don't care whether ordinary members of a church have the right understanding of the nature of the Trinity, say. I'm interested in whether they believe the core tenets of the religion, such as that people go to heaven after they die, or that the universe has an all-seeing and all-powerful creator.
The title question could be considered insulting or at least annoying. If you are having a discussion with a religious person, I highly recommend that you not tell them that they don't believe their religion. They're liable to think you're calling them a liar, and thus to take offence. However, all this doesn't mean that it isn't still an interesting question whether religious people believe their religion. The fact that you shouldn't say, to them, that they don't believe it, doesn't mean that they definitely really believe it.
Caveat: I'm going to mostly talk about Christianity because it is the religion that I am most familiar with, as I have met many Christians.
How to Ascribe Beliefs
How do we figure out what beliefs other people have? I suggest that there are several different criteria for ascribing beliefs. I'm not going to try to define "belief"; I assume an understanding of that. These are just criteria that we use to assess how likely it is that a given person believes a given proposition.
Explicit avowal: Ask a person whether P is the case. If they say "yes", that's a sign that they believe P. If they say "no" or "I don't know", that suggests that they don't believe P. (Slight variant: ask a person whether they believe that P.)
Grounds: Typically, if S believes that P, S will have some justification for P that S could explain, and vice versa. For instance, if Jon is standing in front of a table, in plain view, his eyes are open, he isn't blind, etc., then you can pretty well assume that Jon believes there is a table in front of him, even if he hasn't said anything about it. At the same time, if there is no porcupine in front of Jon, you can pretty well assume that Jon doesn't think there is a porcupine in front of him.
Implications: Typically, if S believes that P, then S will believe the reasonably obvious and direct implications of P (including implications that follow when P is combined with other things S believes). E.g., if Jon thinks there is a porcupine in front of him, then he probably thinks there is at least one animal nearby. If Jon doesn't think there are any nearby animals, then he probably does not believe there is a porcupine in front of him.
Behavior: Typically, if S believes that P, then S will perform the sort of actions that would make sense if P were the case, or at least not do things that would be wildly irrational. For instance, assuming Jon is not suicidal, if Jon drinks from a glass of water, one can assume that Jon does not believe that the water is poisoned.
Emotional reactions: Typically, a person will have emotional reactions that would be apt if their beliefs were correct. For instance, if Jon believes that his child was just killed, then Jon will be distraught. If he isn't, then he probably does not believe that.
Those are the main ways that I can think of that we ascribe beliefs in general to people. Now, how do these criteria apply to religious beliefs?
Religious Belief
Most ordinary people's putative religious beliefs do well with respect to criterion (1) only: people explicitly avow the core tenets of their religions. But on all other criteria for ascribing belief, they appear to not hold those beliefs, or at least it appears questionable.
Grounds: Many religious people (I don't know how many; I haven't done a survey) do not even claim to have adequate grounds for believing their religion. Many say that their putative belief is "faith", which is (often but not always) understood to entail that it lacks evidence or arguments of the sort that normally justify a belief. Some others would claim to have justification (not necessarily using that term), but the justifications they would offer just would not plausibly be strong enough to explain their putatively confident belief. When I was much younger, I used to try to argue with people about religion. One common point people would make is that there is a book about Christianity (the Bible). They seemed to think that an important point in its favor. Also, some would point out that a lot of people (putatively) believe in Christianity. Surely these same people know, however, that there are a lot of books about false beliefs, and there are a lot of false beliefs that are held by many people. Of course, there are better pieces of evidence; nevertheless, the evidence for religious beliefs in general seems much too weak to hold a confident belief in such extraordinary claims.
Implications: Often, it seems that religious people do not believe things that are straightforwardly, strongly supported by central tenets of their religion. For instance, if the Bible is the word of God, then that seems to strongly support the conclusion (once you take account of what the Bible actually says) that it is obligatory to stone people to death for being gay, for committing adultery, for working on the Sabbath, etc. But I don't think that most ordinary Christians believe those things, and I don't think that they are at all likely to adopt those beliefs once you point out the relevant passages in the Bible.
For another example, Jesus famously says that you should not resist evil, and that if someone strikes you on one cheek, you should turn to him the other. But I don't think most Christians believe that.
My point here is not to criticize Christianity for having implausible implications. My point is that most professed Christians do not seem all that inclined to adopt beliefs based on inference from core tenets of Christianity, which suggests that they don't believe those tenets.
Behavior: Religious people very often behave in ways that don't make much sense if they believe the major tenets of their religion. For instance, if I believed that the Bible was the word of God (and the only book that God has given us), I think I would study it very carefully, and make a pretty strong effort to follow its dictates. If I believed Christianity in general, I think I would make a point of going to church regularly. Surely Christianity, if true, would be of crucial import to life. And indeed, some Christians are truly devout. But most, as far as I can tell, are pretty casual about the whole thing. They say they believe in Christianity, but it doesn't seem to be that big of a deal -- not a big enough deal for them to regularly attend church, to carefully study God's ostensible word, or to follow God's ostensible commands when they are inconvenient.
Emotional reactions: Finally, most religious people's emotions do not seem to fall in line with their professed beliefs. I understand that in Christianity, suicide is a sin, so you can't deliberately kill yourself. But if you believe in an afterlife in paradise, then you should be eagerly anticipating death, hoping to die as soon as possible. When your doctor tells you that your tumor is benign, you should be deeply disappointed. When a loved one dies, you should feel inclined to celebrate, or perhaps to envy them. Perhaps you should pray to God to kill you and your entire family.
I don't think most Christians have these reactions. So, on most criteria, the evidence is that most Christians do not believe Christianity.
Quasi-Belief
Of course, it's not as though typical religious people are just big fat liars. They're not like someone who pretends to be a pacifist to get out of the draft, or one who pretends to convert to Islam to avoid being executed. There is something belief-like about their attitudes toward their avowed religion. They think that they believe it. They are not only telling others but telling themselves that it's true.
This state of "telling yourself that P" is not exactly believing that P, but it's not completely failing to believe P either. When confronted with obvious implications of P, you feel some pressure to affirm those implications ... but you won't actively try to draw out implications of P on your own, even if P and its implications are super-important. This is a state in between normal belief and non-belief -- but not, of course, in the way that being 60% confident of P is in between believing and not believing.
Why do we have these different states? Real belief (or "belief" in the philosophers' sense) is for navigating the world; quasi-belief (which might be what the folk call "belief") is for social bonding and forming a sense of identity.
When you think about this, it raises the question of how many other putative beliefs people have are not "real" beliefs. Maybe most philosophical beliefs in general are only quasi-beliefs? Maybe political beliefs are only quasi-beliefs?