Or maybe I'm not very good at explaining it either
Forget about God as a literal supernatural being, JP is using it as a metaphor, really as a metaphorical truth. Brett Weinstein coined this term to mean "a belief that may not be factually/scientifically true, but believing it in practice turns out to be beneficial due to the behaviours it results in."
JP is using god as the metaphorical truth that underpins a worldview. He isn't doing this in a gotcha sense, but to argue that god is really just a utilitarian concept that helps transmit culture. In this sense it doesn't really matter if god exists or not as his utility draws from his functional role in underpinning culture, rather than supernatural powers.
You object to him framing it as 'SH believes in god', whereas he could equally frame the idea as 'God isn't really what you think it is. His value comes not from literal existence, but from his ability to underpin cultures and enable transference of ideas between generations. Atheistic cultures also have something which serves this role: the functional equivalent of god'.
An example:
Locke was a Christian liberal. He believed liberalism worked via Christian Divine Providence
Jefferson was a Deistic liberal. He believed liberalism worked through Deistic Divine Providence
Condorcet was a secular liberal. He believed liberalism worked through secular, teleological Progress
They basically all believed in the same thing for pretty much the same reasons. Just one happened to be atheistic, and the other 2 theistic. 2 metaphorical truths that relied on god, one that didn't. All are metaphorical truths though.
So Locke and Jefferson have 'religious' belief on this issue, and Condorcet has a 'religious-type' belief (a non-religious belief that replaces a religious belief i.e is functionally equivalent to a religious belief).
JP is saying we all have either religious, or religious-type beliefs, and that the distinction is trivial. Alternatively, we all rely on metaphorical truths.
JP also believes the Christian God is what underpins Western classical liberalism, and believes that when New Atheists attempt to destroy this foundation, this risks the entire belief system, his 'chaos'. He advocates acceptance of the metaphorical truth of the Christian god as a method for preserving Western society.
Hopefully that makes sense