@ByGrabtharsHammerWhatASavings
Most of what I've seen him say is overtly sexist I'm afraid. His main talking point seems to be that 1) women are biologically predetermined to be better at caring jobs and men are biologically predetermined to be better at maths, engineering, and being the boss. 2) The kind of work women are innately drawn to is objectively easier, less valuable, and lower skilled than the work men are innately drawn to, therefore those jobs will always command a lower wage. 3) Men will therefore always earn more than women and there's nothing anyone can or should do about it, the wage gap is feminist progaganda, and women would be happier if they could just learn to accept their naturally place in society. This of course, all backed up by a massive dose of evangelical Christianity. Not much for a feminist to find common ground with there I'm afraid. Even the trans stuff is coming from a different place - we want to unhitch gender from sex completely and let men be freely feminine, he opposes transgenderism because he wants gender to be inseparable from sex and thinks everyone should stay in their original box. The man is odious.
A lot of what you say only shows how what he says is misrepresented.
I don't believe he has ever said :
1)
women are biologically predetermined to be better at caring jobs and men are biologically predetermined to be better at maths, engineering, and being the boss
He has said that the psychological data of the big 5 model suggests that women are more empathetic / caring etc.. "more interested in people" is the way he often describes it, and that this explains why they go into nursing / caring roles. This is contrasted that the same model shows that men tend to be "more interested in things", hence the preponderance of men in engineering stuff.
2)
the kind of work women are innately drawn to is objectively easier, less valuable, and lower skilled than the work men are innately drawn to, therefore those jobs will always command a lower wage
I have never heard him say these jobs are objectively easier, less valuble (in a moral sense) or lower skilled. What he says is that caring roles are inherently unscalable (you can only care for a certain number of people at any one time) and this limits the potential revenue, whereas engineering type roles (say, software) can scale up to a much greater degree to earn greater revenue.
he opposes transgenderism because he wants gender to be inseparable from sex and thinks everyone should stay in their original box
Again, I've never got this from his work. He has always framed it as a free speech issue, not that trans people shouldn't exist or don't have the right to exist. He has expressed plenty of times that he has used his trans students' preferred pronouns when asked, but objects to being legally coerced into doing so.