"Alt left" is of course derived from the alt right. It's been used in a variety of ways. Some centrists use it simply to suggest that the far right and the far left are similarly violent, extremist and evil—in that context, it's simply a form of red baiting. It's also transparent nonsense. The far right in the US is far larger and far more violent than the far left is or really can ever hope to be. There are a handful of honest to goodness Stalinists on twitter, if you look for them, but they have no power and no hope of ever getting any. Jill Stein is kind of an idiot, but she is not in any way comparable to Richard Spencer, and it's simply deceptive to pretend otherwise.
Other people use the term "alt left" in a more specific way—to refer to people on the left who oppose political correctness and engage in trolling analogous to the kind of online shitposting characteristic of the alt right.
The problem with this is that the alt right are not really defined by shitposting. Nor, contra Angela Nagle, are they defined by opposition to identity politics or political correctness—if they were, Jonathan Chait, Mark Lilla, and Nagle herself would all be members of the alt right. Dislike of political correctness—which is to say, sneering dismissal of the concerns of marginalized people—is a popular position, especially for white people, of every political persuasion. That is bad—and it is especially distressing to see it gain some traction on the left among so-called Marxists like Nagle and folks around Jacobin or Chapo Trap House who should know better. But, again, it's not what the alt right is about.
The alt right is defined by white nationalism. They're Nazis; they're the KKK. The "alternative" they offer is an alternative to a mainstream conservatism which, for all its dogwhistle racism and general despicableness, still pays lip service to ideas of equality and freedom for all. The alt right does not. They believe in rights for white people, and genocide and ethnic cleansing for everyone else. That's what the alt right is. Trolling online or marching in the streets are just tactics. The core of the alt right is Nazism.
There's more than a little Nazism in the conservative party in the US, and in American life as a whole. But different things are still somewhat different, and Mitt Romney is not Barack Obama is not Donald Trump. Fighting Nazis is important, and you can't fight Nazis if you have convinced yourself that the Nazis aren't any worse than Mitt Romney, or Hillary Clinton, or Bernie Sanders, or whoever. Labeling Nazis accurately is vital because fighting Nazis means forming alliances with whoever will fight them with you. If you are too eager to label everybody you disagree with a Nazi, you're going to hamstring yourself.
There have been some putative leftists on twitter saying that neoliberals and centrists are the same as Nazis. This is bullshit, and they should stop it. Jonathan Chait is, I firmly believe, a piece of crap, who should be hooted on most occasions. But he's not the Daily Stormer. Similarly, leftists kicking identity politics and claiming that anti-racism and feminism will distract from the work of winning the white working class—those people suck, and should be told that they suck. But they aren't Richard Spencer (even if he praises their books) and the distinction is an important one.
The term "alt left" creates a false equivalency, which bad actors, from Chait to Donald Trump, can jump on and use to undermine anti-fascism. It's an imprecise and deceptive term, and it hurts the left, and anyone who is committed to anti-fascism.
People have asked me what term to use instead. If people are looking for an invidious term with which to label the entire left, I'm the wrong person to provide it, since I'm a leftist, so I mostly think of the left as "the people who you should listen to." If people are looking for a term to describe the anti-PC, anti-ID politics left, I think "dirtbag left" works. That's the term folks like Chapo have chosen for themselves, and I don't see any pressing reason to come up with something they don't like just because they don't like it.
The main point, though, is that the president is using alt left to red bait and to support fascists. Folks of good conscience shouldn't want to be associated with that. I never liked the term, but it's certainly going to cause more harm than good going forward. It's past time to dump it.