Can someone explain to me what Jordan Peterson's beliefs?

His biblical lectures have been absolutely addictive, from a literary perspective.

I'd recommend them to anyone interested in writing fiction, especially atheists, because the bible is apparently the motherlode of character archetypes.
 
Reacting to your earlier point, Jordan Peterson believes a correlation between sex and gender, and he balks at the "gender unicorn," which is honestly a pretty noncontroversial idea - that emotional attraction, physical attraction, gender identity, gender presentation, and sexual characteristics are five different aspects of a person.
They may perhaps be noncontroversial but in the grand scheme of things how much actual societal weight needs to be afforded them, is another thing entirely. Personally, I've always been bemused by the idea of stating a preference for one's likes ( as if one's tastes don't fluctuate over time in all manner of areas, especially attraction) and even more so at any attempt to codify such disparate matters.

He also suggests that the whole gender-neutral pronoun thing is just "using" trans people, and claimed that a large contingency of trans people are actually opposed to this, when in fact in my experiences, trans people are often fairly supportive.
I would presume there exists some statistical research on the subject tbh, so personal belief is kind of irrelevant. If it can be tracked, it can be assessed. Anything otherwise is merely anecdotal speculation.