I don't want this thread to become an argument about the existence of God, and whether belief in God is a hinge. If you want to consider whether belief in God is a hinge, please do it in another thread. That said, I will partially answer the question about whether belief in God could be considered a hinge in the Wittgensteinian tradition.
The Christian in acting their life cements the hinge "God as the ultimate source of all power", which is their truth. The Atheist in acting their life cements the hinge "there is no God", which is their truth. The Agnostic in acting their life cements the hinge "it is impossible to know whether there is a God", which is their truth. — RussellA
There is no doubt that Christians and other religions consider belief in God a hinge belief or foundational conviction. There is also no doubt that such language games exist. But just because there are language games that express these ideas doesn’t mean that all language games have equal footing. Some language games have a much better grounding, and we are constantly revising them.
However, the question of whether belief in God could be a hinge in the OC sense is an interesting question. Consider the following: “God exists” might ground certain practices like prayer, morality, and cosmology in the same way that “The Earth exists” grounds geology. Doubting that “God exists” would unravel the entire language game of many religions, just as hinges would unravel epistemology.
Also, for many, “Belief in God” isn’t up for debate within their lived belief system. It’s not a hypothesis that’s tested (for many) it’s a conviction that’s lived.
On the other side of the argument, “I have hands holds across contexts and language games. Atheists function without belief in God, but how would they function without the belief we have hands? Moreover, belief in God is doubted by many, and it’s debated in theology and philosophy. Wittgensteinian hinges resist doubt (OC 19 “incapable of doubting”). The belief that God exists invites doubt, even among those who believe.
I would say that in some cases, especially if someone had a direct experience of God, it could be a hinge for them. I think consciousness is a hinge, and if consciousness is fundamental, then it could be considered a hinge. Moreover, some might argue that consciousness/mind as fundamental might
be God. I’m not sure, although I believe consciousness is fundamental.
There’s much more that could be asked and questioned, but this subject should be in another thread.
Your question
@RussellA is a good one and is being debated by some philosophers.