Most people don't see the logical or metaphysical connection between PSR, PNC, essentialism, etc. and theism. All they see is that theists employ them when arguing in support of theism and that's enough basis for them to reject those principles without further consideration. (Professional philosophers are more likely aware of the implications both ways, but I'm not talking about them right now.)

I personally have no theistic or religious upbringing myself, but I always thought those principles were simply common sense and therefore not objectionable in any way. Without having ever debated theism (where I live, there are just a few old church-going people, no theists in the relevant sense, certainly no outspoken ones), I did not see any direct connection to theism. The implication of theism became increasingly felt only in small steps, as I was gradually broadening my worldview and amending it for coherence and consistency. Then at some point a threshold hit that necessitated consciously facing one's own conclusions. I tend to assume that most people don't care about the consistency of their own worldviews enough to arrive at that threshold.

RomanJoe wrote:

Just curious, what initiated this broadening of your worldview?

It broadened as I kept thinking things through. Nothing initiated it. It was something I always felt compelled to do, so much so that all other things were less relevant. We can call it destiny.

I don't think theism per se is common sense. It follows from common sense, because it follows from PSR, PC, etc. but not everything that follows from common sense is also common sense. There have existed past cultures that were not theistic at all. Maybe it stemmed from a lack of analysis and careful consideration of the world, but still, it's different. Theism is true and I take it to be a very certain and simple truth that we can know beyond a reasonable doubt, but I don't think it is comparable to stuff such as "there exists an external world", "other people have minds", "every effect has a cause" "every fact has an explanation" etc.

However, you are correct that in general people only ever reject psr and pc because of theistic implications. It's entirely ad hoc, but since many atheists don't want God to exist and see no apparent internal contradiction in denying PSR, they do it when pressed or presented with cosmological arguments. I know of pretty much no other situation in which anyone is willing to accept a "brute fact", it only seems to happen in the context of cosmological arguments.