I'm genuinely curious as to where you draw the distinction between one or the other, since from my perspective I simply do both.
I'm sure you do, but these people don't. Notice that SJWs are, about hunting down incorrect thoughts and belief systems, not fixing societal problems. "White Supremacy", "Patriarchy", "Transphobia" etc. etc. are not things that people do, they are things that (according to them at least) people think, or at the even greater extreme, what they are. Consider also the "cancelling" and "deplatforming" of individuals guilty of such wrongthink.
It's not about what actions their targets take. That's why apologising to them doesn't work, they have judged your character and you have been found wanting. No matter how much money PewDiePie raises for charity or whatever other good things he does, he is and forever will be a Nazi according to ResetEra and similar groups. Nazism has been judged to be part of the essence of Pewdiepie's being, in a sort of Platonic/Aristotelian sense. His actions no longer matter.
This Platonic essentialism explains the weird "original sin" aspects of modern Leftist ideology. If you are white, you are guilty of "whiteness" and oppressing minorities, even if you have never done anything remotely close to oppressing anyone. What you did doesn't matter. If you are white, the oppression isn't in your actions, it is in your nature. You shitlord.
Compare this to the "Old Left". They didn't care what was in your heart, they cared about action, about policy. Equality to them wasn't about purging impure thought, it was about redistributing wealth, trade unions, nationalisation, wage controls. Things you actually left your basement and did. You proved you were a Leftist by doing Leftist things, not by telling everyone just how very Leftist you are but it's ableist to actually ask you to do anything (cf Clawshrimpy).
I think the current state of left-wing politics has more to do with the collapse of the Soviet Union and the general presumption that Marxism and Socialism are now harmless, allowing much more free discussion of the topics. It also probably drew in people who prefer to think of themselves as underdogs, on top of the fact that openly supporting Communism has been a common act of rebelliousness and counterculture dating back to at least the 1930s. The real shift is demographic, not moral. Communism, Socialism, et all were originally championed by middle-to-working class people, with only a few core academics at the top to drive rhetoric. Now, overwhelmingly the people who are likely to identify as Socialists, Communists or Marxists are overwhelmingly middle to upperclass, and a large number of them are on the younger side.
There's a potential arguement to be made that the rhetoric of the modern left wing is some kind of coping mechanism to deal with white guilt, survivor's guilt, and anything generally designated as "priviledged". I'm more inclined to think of it as another outgrowth of this strange wave of emotional behavior we're seeing across the masses, which involves not only politics but has affected other things such as art, aesthetics, humor and entertainment.
The Twitter Progressives owe a lot more to the mechanics of Twitter and the culture surrounding it than they do to any sort of moral thought on the part of the people actively posting there. This has been true of the internet at large for quite some time but Twitter just happened to distill that set of mechanics down the most efficiently. Posting regularly online is habit-forming, and it feeds into a sense of community that generally most people are lacking in their lives. Its not that surprising that people already leaning on one ideology would fall to dogmatism on a site where your thoughts and words at limited to singular 240 character posts.
The mechanics of Social Media, Twitter in particular, I think have played a major role in the shift of thinking. My sperg-out in the OP talked about what I think has changed in the way that leftists think, but not really why. I think everything you've pointed to here is probably correct. Twitter, though, is a particularly interesting case of how altering the structure of how people engage with each other can alter their thinking and behaviour.
The two features of Twitter that define how it is used are the forced brevity of its messages and the ease with which you can block people.
The former prevents ideas being exchanged in any depth. There was a reason Socialists and Communists used to have a reputation for droning on and on for hours, and that's because those ideas are complex and long-winded. So Twitter discourages that kind of idea, and encourages sound-bite ideas without any explanation. "Pewdiepie is Alt-Right" is a brief, authoritative-sounding statement. It is also complete nonsense, but it takes more than 140/280 characters to explain why it's nonsense. So the simple, broad statement about the "nature" or "character" of an individual or group becomes the easiest form of political discourse, rather than long screeds about how the proletariat can seize the means of production in the era of State Corporatism.
The latter (the ease of blocking people) makes it simple to eliminate all dissenting voices, surrounding yourself with an echo-chamber of people who share your ideas. Of course, with no dissent comes no debate and nothing to talk about, so the only way of creating debate is to turn on your friends and accuse them of not being as ideologically pure as you, leading to purges and purity spirals. And because Twitter makes it impossible to have a proper debate, you just get hot takes and "x is a Nazi" statements.