I think when you say liberals you mean progressives - typical democrats. Which are neither liberal nor left but far right. They dont care about civil rights, freedom of speech, free markets and so on. You know, liberalism.
Now, i think its obvious that they are not liberal in any sense of the term. Far right? Yes, their redistribution is a far-right process. Wealth redistribution is not inherantly left. It can be if it benefits the poor, its not if it is done along arbitrary lines about intrinsic charackteristics such as race, sex and so on instead of actual need and ability.
And i would argue american liberals - aka republicans and libertarians - are further to the right than european liberals at the very least.

As for what liberal means in europe, well, some so called liberal parties are more to the right, they arent usualy seen as actualy liberal. They would be libertarian, but thats not a term commonly used here. Liberals tend to be left in europe, as is sargon. He mightve shifted a bit to the right, in one political compass a while ago he agreed to "From everyone according to his ability, to everyone according to his need" - in a later one he rejected it, i dont think he actualy does to be honest, just today he had a stream in which he defends social safety nets - now, id actualy argue against social safety nets. Not becouse people shouldnt be able to live, no, becouse i would argue for an unconditional base income for everyone. One you can live from. Not with to many luxeries of course.

There was something recently, it wasnt about him being right. Yes, they called him alt-right... Yes, sargon. sure.... what they hate about him are two things: a) that he is a liberal and b) that he doesnt agree with the alt-right. Which also means he doesnt agree with them. Their believes are the same, just the priorities differ.
You can look at groups such as women, miniorities and the like - OR you could be a liberal and look at individual people.
I honestly fear for asians and jews as both the alt-right and the progressives can agree on them as targets. They are privileged and outearn us. The same old story, the justification back in the 30s/40s, during the time of segregation and so on.
Oh and, the average IQ is different for different races. Which is also a problem for you if you are worried about the wage gap. Becouse that means you look at people as groups, not individuals.
Whereas a liberal can just not care about that as a low average IQ doesnt mean every individual has to be low. Soooo you can still take the doctors and the like without bringing on the alt-rights horror story.

As for peterson, i think, yes, they will disagree. Though not about the points you criticised about him. Im sure on "petersons views on transgender people" - which by the way is something between neutral and... not positive but he wants to help them - they wont disagree a lot.