I would also point out that modern comedians get hella offensive* whenever they want and they still succeed. South Park, everything by Seth McFarlane, Archer, Always Sunny in Philadelphia, most standup comedians, most prank shows as well as Tosh.0 which is in a similar vein, Big Bang Theory (it sucks but its also pretty offensive). Even like Tina Fey, who gets called out as a SJW, really really isn't, she's pretty much just a female version of the average male comedian with everything that entails.
I would say that real leftist/Millenial/SJW comedy right now centers around the principle of punching up instead of punching down. Jon Stewart's daily show and all of its descendants, Key and Peele, I'm struggling to think of any other paid American examples off the top of my head. Lot of internet stuff tho, which makes sense since AFAIK few millenials have broken into major entertainment industry roles as of now (with exceptions like Alex Hirsch although even he would barely count as a millennial by most standards). There's also a lot of humor that either doesn't use specific people as the butt of its joke, or is "for" the same group its making fun of. For example Pearl in Steven Universe has a lot of jokes that are targeted at mentally ill or mentally unhealthy people but she comes across more as relatable than mean. To the point where I would say neurotypical people probably enjoy the character less rather than more. Compare say Sheldon Cooper in the Big Bang Theory. Where like yeah he references a lot of geek culture and yeah the actor has gone on the record saying he's autistic but the character exists for outsiders to point and laugh at both geeks and people on the spectrum.
*or "offensive" with air quotes, or just black comedy that pushes on sensitive issues. I'm using the word without judgement for this post.