I do, I have! The gods know I change my mind!
But it's always because I have heard arguments that logically implies that the position I currently hold is wrong! With religion we are talking about adopting an unprovable idea (at least until I die/the rapture/doomsday/repeatable miracles).
What do you mean by "logically implies", though? You mention heliocentrism as a belief you would be unprepared to give up. Yet there is no "logical" proof of heliocentrism - only arguments to the best explanation of the evidence. Why do you assume that religion is unprovable in that way? Religion isn't a single idea - it is many ideas, and perhaps more importantly, there is more to it than ideas, too.
I don't think that people really believe what they believe because of arguments, logical, evidential, or otherwise. Although people may
believe that they believe things because of such arguments, I think that most of the time they believe what they believe because it meshes with their experience. For example, most people believe politicians and lawyers to be inveterate liars not because there is good evidence for this, but because that belief fits in with the narrative that they tell (perhaps subconsciously) about the way the world works. (If evidence supporting this belief emerges, then so much the better, but it's not the reason for the belief in the first place.) Religion is the same. People believe in (for example) God not because there are good arguments for God's existence - although when asked they may cite such arguments - but because the belief and, crucially, the practices associated with that belief, reflect their own experience of life. People come to believe in God because they come into closer contact with the belief and the practices and find that they reflect their experience of life. Conversely, people cease to believe in God because they find that they do not. Arguments for or against are really secondary for most people.
I still don't see that I would abandon my understanding of, say, a heliocentric world in favor of a geocentric world view, even if I was surrounded by lots of geocentricists. And unless they put me to the stake I doubt I would claim to change my belief.
And even more, if I changed from one religion to another, because not doing so was to much effort, then that wouldn't necessarily mean that I actually believed in what I told others, simply that I would say I did.
The problem here is that the geocentrism/heliocentrism example isn't really parallel to religious belief, because religious belief is not the same thing as normal propositional belief.
There are different schools of thought regarding what religious belief is. Some people (mainly atheists) think that religious belief is purely propositional or cognitive, exactly parallel to scientific belief. So when a believer says "God is three persons" she is making exactly the same sort of statement as when the scientist says "The Earth revolves around the Sun", and these statements can be evaluated in precisely the same ways. At the opposite end of the spectrum there are people (mainly theologians) who think that religious belief is wholly non-propositional and non-cognitive. On this view, when the believer says "God is three persons" she is not making any claim about reality at all - she is merely expressing a sort of feeling, or something like that. This view is similar to expressivism (the meta-ethical theory, now much out of vogue, that moral statements such as "Murder is wrong" are not making claims at all but merely expressing the speaker's feelings). So on this view, religious claims can't be evaluated in the same way as scientific ones, because they are completely different kinds of utterances.
I think that as usual the truth is somewhere in the middle and that religious beliefs have both cognitive and non-cognitive elements. To believe in (say) God is partly to believe something to be true in the propositional sense: it is to believe
that a certain entity objectively exists and has certain properties. But it is
also to place faith in that entity - it is to believe in him in the sense that you believe in your friend. It is to take up a certain existential attitude, one that manifests itself in (but is not reducible to) certain activities such as prayer, participation in liturgy, and perhaps following ethical standards. Robert Audi (among others) has argued for this complex understanding of the nature of religious belief. If that's so, then to believe in a religious claim involves much more than merely to hold that a certain assertion about the universe happens to be true, after the model of a scientific belief; although it does involve that, it also involves the way you live your life. That is why losing a religious belief is typically a traumatic experience, because it requires not merely that you adjust your metaphysics but that you change your life. Conversely, to change your life is, in part, to change your religion, because that is what religion (partly) is.
That is what underlies what I said about people changing religion because it's less effort. I didn't mean that they just say they believe something because it leads to less social hassle. I meant that if they are socialising with people of that religion, perhaps taking part in events associated with it, or even living in a society where that religion and its practices are widespread and highly prominent, then inevitably they are already living their life in a way that reflects the beliefs of that religion (even if they do not believe those beliefs to be true). But the nature of religious belief is such that to hold a religious belief is, in part, to live in a certain way. This means that these people are already doing half of what it is to hold a religious belief! It's like they have one foot in the water already, simply by being there. That leads to cognitive dissonance. If you act in a way that doesn't reflect your inner beliefs, something has to give - you have to stop acting that way, or you have to change your inner beliefs to match. In the case of our hypothetical person surrounded by the religion and partly participating in it, cognitive dissonance may lead them simply to accept the beliefs whole-heartedly rather than in this uncomfortable half-and-half fashion. And I don't mean that they cynically choose to adopt the belief or pretend to, or even that they sit down and consciously decide to believe it (something which I don't think is generally possible). It's a process and one that happens largely subconsciously, until one day they realise that actually, yes, they do believe after all.
That's how I see it anyway. I may be wrong - this isn't the sort of stuff I know much about.