If left to themselves in meditation for a very long time, do you think an INTP and an INFP would arrive at a similar conclusion of the existence of god? Or do you think both personalities would veer off in completely different directions? In the end, does logic hold any difference over emotion?
I think religiosity is a trait that any type can have. There are tons of examples of INTP theologians, or theologians who have relied upon Ti to create proofs of the existence of God. Aquinas is an example that comes to mind immediately. I think that Ti is going to approach faith with the same probing curiosity with which they explore any other subject, going deeper and deeper into the nature of the universe until they come to a point where they either arrive at some satisfactory conclusion about it.
My guess would be that an Fi-dom is more likely to approach God from an ethical than material standpoint. If Ti is likely to look for God in the search for a prime mover, then Fi is searching for moral order as exemplified by the Kantian perspective. Fi is searching for some basis for their own innate sense of right and wrong, and a justification for their sense of ethical normativity more universal than their own personal feelings and direct experience. An Fi-user has a feeling they know to be correct, and then is going to use Te to find the grounds and consequence for that. They can, of course, find something inherent in the action itself, and have no need for God. But if they're inclined towards it, an Fi user is more likely to intuit directly that God exists, and then reason backwards from that point to determine what it means if God doesn't and whether we're better off because of it. Blaise Pascal of the famed Pascal's Wager exemplifies this kind of logic when he argued that the wise decision is to wager that God exists, since "If you gain, you gain all; if you lose, you lose nothing".
Are the conclusions of modern thinkers with the backing of math and science any less sophisticated than that of nomads?
I think this is an interesting question. I'm not certain whether reasoning about the existence of God is as compelling to examine as the moral codes that are particular to individual cultures, and those that transcend culture. Isolated tribes living in remote regions can have moral lives as complex as those of highly advanced Western societies, even if the values comprising those moralities differ. People try to explain their world, their place in the world, and how to live well in it to the best of their ability. Logic is transcendent: a careful and analytical mind in the most isolated parts of Amazonia ought to be able to reach the similar conclusions with the same set of assumptions as a philosopher at Cambridge, even if the Cambridge philosopher might reach that conclusion more readily because she has the benefit of formalized convention at her disposal. A less critical mind is going to come to equally unsophisticated conclusions, as evidenced by the shit ton of mindless Fundies living in some of the most technologically advanced societies on the planet.*
I personally am an Fi-user and am of two minds about God. I believe that the inherent good of certain actions makes them objectively better without the need to reference any external source of virtue. There is no moral necessity for God, in other words. At the same time, I feel equally strongly that I have a soul, and that soul connects me to something greater than myself. I don't why I feel this way, don't have anything credible to support it, but
know it to be the case. As an Fi-user, I also don't feel like it
has to make sense to anybody but myself, because it's such a personal thing. It's why I continue to identify myself as Catholic even though I think a lot of Catholicism is make believe. I want to honor that part of myself that's mine but not entirely me with ways and rituals that make cultural sense to me.