If you're saying that Peterson doesn't "act out," unlike most theists and atheists, because Peterson is more self-aware and cautious, you're only proving my point about Peterson's condescension. You're just trying to explain how Peterson's superior to most theists or atheists.
Either way, this is obfuscatory. It's very simple: you either believe the natural universe was created by a perfect person who still performs miracles or you don't. You're either a theist or an atheists at the level of belief. You can say you don't know because you haven't decided, but what Peterson does is hide behind red herrings.
Your first paragraph looks to me like a Petersonian red herring. Atheism requires a "higher level of cognition"? All of us already have a higher level of cognition: it's called personhood as opposed to animality.
Sure, there's plenty of room for hypocrisy from theists and from atheists. Lots of theists say they believe in a higher moral power, but they act like crude, myopic consumers. And some atheists say they believe there's no such higher power even though they act heroically and can't personally account for a moral law.
But that's a distraction from the issue at hand. Does Peterson believe the monotheist's God is real or not? I've seen him go on and on at this point. He'll be like Bill Clinton and say, "It depends what you mean by 'real.'" He'll try to reinvent the wheel, and say you have to solve the riddles of metaphysics and truth and facticity to know what we could possibly mean by saying that God exists. And of course that's already been done in the long history of the philosophy of religion .
Peterson is just dodging the question, hiding behind his ignorance or the fact that he hasn't made up his mind or is afraid of his answer.
I'm not saying he has nothing interesting to say. But you should be aware that gurus tend to disappoint in the long run. No one deserves to have such power over others, and practically no one can exercise this power with honour.