Edit: If you believe in a religion, then religion exists in the most real sense possible, as that which guides your relation to the beginning and end of reality itself, God.
If you don't believe, then religion exists in no more and no less of a sense as capitalism: it is a fiction which vast amounts of people believe in and live their lives by, and so it is real. Not in the sense of the computer in front of you, but in the sense of a real social relationship. From a secular standpoint religion and capitalism have no more and no less reality than other fictions like gender and race.
This is an excellent comment, and I agree on the conclusion that either exists as much as the other.
However ;-), I dare to say your argument is weak: Assume "I believe in the apple on my desk". But you will find there is neither a fruit nor an Apple branded computer on my desk. So an outside observer is bound to believe I am going mad, hence my belief shapes my social relationship with others around me. Now does this make the apple as real as religion, which becomes real due to it's impact on social relationships? Or are people who let religion shape their social relationships as mad as I am? Or is the argument flawed? (edit: No, I can not answer these question).
Shapiro's "Thinking about mathematics" springs to my mind, IIRC in the first chapter(s) he gives a nice overview about what philosophers thought about numbers, the realm of numbers and whether they "exist" or not. I think some of that could be applied here. (And, generally, I think it's a great read for computer scientists & mathematicians interested in philosophy, as it gives a great overview across various different schools).
I think the problem with your argument is that you're replacing the concept of religion with the concept of 'apple' which in every sense signifies something that exists as a hylomorphic object. An apple which can sit on my desk. However language is full of concepts which don't share that kind of existence, ones which tend to be the objects of philosophy. Love, justice, power... race, gender, capitalism, religion, God. These exist but not as 'physical' objects, objects whose existence can be accepted or denied according to empirical criteria.
For example, in the market I can say I see capitalism before me, even though it's not a physical object. It's in the exchange of goods, the extraction of commodity and surplus value. In the same way in a synagogue or church I can say that I see religion before me, or in the Oval Office I see power (as well as in the streets, of course).
With respect to comparing God to an apple, I'd take a Kantian line. One refers to belief, the other to knowledge. Got to make space for one in order to have room for the other ;)
Absolutely :) Very convincing, but as per your user-info (should have read that before trying to be smart), I should not expect less of someone with a proper philosophical education and the (as I suppose) accompanying repository of philosophical knowledge ;) The subject of your thesis seems pretty interesting,... ah, I'm digressing ;)
Now, regarding Gods and apples: Because that's how I setup the Gedankenexperiment (and assuming I belong to the majority of people, who are neither blind nor suffering from severe neurological problems), if there was some matter in form of an apple on my desk, I should perceive it. IIRC Kant would say that I have a-priory knowledge of the absence of an apple from my desk.
(I'm afraid I can't argue against that, so let me rephrase the first paragraph until I come up with something useful on how to convince you that comparing religion to an non-existent apple is perfectly fine reasoning.)
[... some minutes passed ...]
No, I think you're right. The problem is that, as you say, an 'apple' is an inherently physical object. Hence there either is one sitting on my desk and I can see it, or I can see that there is none. I can not just bend the definition of an apple at will, so I think I'm stuck here; accordingly, when I say "I believe in the apple on my desk", I am basing my proclaimed belief on a verifieable-false proposition; and much as with false assumptions, from that I can obviously derive anything.
Religion (or other constructs of the mind) don't exist as physical objects (there is no religion-shaped matter), yet they influence and shape (ha!) our world, often even beyond what's possible for a physical object [1].
edit So when I say that I still believe in the apple on the desk even if there is proof of the contrary, I am just acting like an idiot - and that's what's actually influencing/shaping my social relationships ;) end edit
But, one ray of light :) Comparing religion to an apple might not be possible, but I think it's undecidable if comparing God to an apple is: What constitutes God is a matter of belief and hence there is no coherent definition. E.g. some might say there is no physical God, or maybe there is one but not "on our realm of existence" (whatever that means). OTOH, some religious people might even go as far to say that there is a physical heaven and a physical hell, even when presented physical proof of the contrary. So, maybe, there is an apple after all? ;)
[1] I can't resist but to note that, if we were on Pratchett's Discworld, this would be much easier. In that case "the Gods" would probably come knocking on my door for implying that they might not exist.
Edit: If you believe in a religion, then religion exists in the most real sense possible, as that which guides your relation to the beginning and end of reality itself, God.
If you don't believe, then religion exists in no more and no less of a sense as capitalism: it is a fiction which vast amounts of people believe in and live their lives by, and so it is real. Not in the sense of the computer in front of you, but in the sense of a real social relationship. From a secular standpoint religion and capitalism have no more and no less reality than other fictions like gender and race.