Bill Maher had a show called "Politically Incorrect" throughout the 90s. The word had wide use in both liberal and conservative circles. While the right used it more frequently against the left as a talking point, that doesn't then transform it into the term "cultural marxism," which is in itself incredibly loaded. Your analogy is literally just "both words were used by the right against the left, therefore they are the same." This is not convincing.
You say "regressive left" is a fantasy term used to describe two incoherent ideas: that the left opposes free speech, and that the left opposes free exercise of religion. I agree with the later - anyone using the term to describe the free exercise of religion, in terms of being able to freely discriminate against other religions, is off the deep end. But the focus on free-speech is not a non-issue. Colleges increasingly deplatform (there is statistical data) speakers due to leftist student protests. When cartoonists who draw Muhammad are killed, the left is filled with individuals speaking up about how the cartoonists shouldn't have drawn it, and that it was their own fault. In Canada they're putting in place (or have already) "hate speech" laws that give tremendous fines for not using proper gender descriptors including ones like "zie/hir." Kirsten Powers, Jordan Peterson, Maajid Nawaz, and Jonathan Haidt are all liberal/moderate intellectuals, among others, who are worried about this problem, so you characterizing it as libertarian atheist hogwash is more than disingenuous. I mean the term itself was literally coined by a liberal, Jonathan Chait, so it's pretty damn ironic to be thinking it's some conservative plot to undermine liberalism.
All of your examples are anecdotal. You say "there is statistical data";
produce it. Show me a peer-reviewed study - something genuinely high-quality - that indicates that this is an increasing problem, or that it is specific and unique to the left. I do not think you can. The data isn't there, because this is, indeed, a fantasy - pure hogwash pumped out (largely) by a conservative machine determined to discredit the opposition via whatever lies it can.
It is convenient for some liberals who want to be seen as "reasonable" to buy into this fantasy, to present themselves as the "good liberal" in the landscape of that vapid fantasy hopes of winning some readership among conservatives; since the accusations are entirely groundless fantasy, after all, it involves no real sacrifice beyond And, of course, there are always dumb people at all points of the political spectrum that ideologues can pull together into anecdotal smears that are eagerly swallowed by anyone who wants an easy answer; but there is no evidence whatsoever that that kind of silliness is on the rise, or that it's any more common among the left than the right.
For the record, you are incorrect about who coined the term. It was coined by Maajid Nawaz, an anti-Islamic activist, as a way to tar the political left for being insufficiently anti-Islamic, and adopted by (as I said) right-wing libertarians looking for a way to present the left as "other" in order to substitute for the increasingly-tired accusation of Marxism. In short, it is pure, unadulterated hogwash spun by bloggers and think-tanks to trick rubes into agreeing with them. Its functional purpose in an argument is to give conservative-leaning atheists a thin veneer of intellectual-sounding cover by giving them bits of meaningless, important-sounding jargon they can pull over their attempts to clobber their ideological opposition. It doesn't even take much investigation to turn up how vapid the accusation is - there's literally nothing behind it beyond red-faced conservative talking heads vaguely waving at whatever the stupidest people Fox News could drudge up to throw onto the screen as a strawman against the left. There's no data supporting it, no coherent framework describing what the conservatives freaking out over it are actually afraid of, and no connection whatsoever to anything the left as a whole actually does or believes.
You're also whitewashing what the term means; it is
specifically an anti-Islamic slur (saying that the left is too accepting of Islam), not a general statement about no-platforming or whatever the buzzword floating around on the blogs you read today is.
It doesn't have even the tiniest relation to reality. Like the breathless obsession conservative think-tanks had with their manufactured controversy over "political correctness" in the 90's, the accusations you're talking about are pure spin, nothing else.
(Again, don't you feel even the smallest twinge of concern that you are presenting your buzzwords about what-you-think-the-left-actually-believes to, well,
leftists, and being told that it has no relation to reality at all? If it was a serious accusation - if it reflected reality in any meaningful way - you would find people willing to defend it, not people pointing out that you're full of shit and your buzzwords are dumb.)
It's nice of you to disqualify a source as reputable at-will. Such sublime argument.
Come on, man. "Here is a blog that agrees with me!" isn't a reputable source. Anyone can pull any blog they want out of their ass.
We can legitimately disagree about a lot of stuff, but if we want to talk seriously about political-science in a way that can cross the aisle, you need to be willing to put in the actual work, which means going to peer-reviewed journals and listening to what they say (and, ideally, not just taking one or two studies out of context, but reading a lot of them to get a general sense of the state of a particular field.) It's hard work and it tends to not produce easy answers or snappy memes like you were trying to slap people with above, but it gives you better answers, too. "Some blogger is mad at the left for something" doesn't tell us anything. You're trying to make sweeping statements about an entire political perspective that encompasses a huge chunk of the country.
This gets back to what I was saying above about why these kinds of memes are so popular with a certain segment of geek culture - again, there's the desire to sound like you have a deep, thorough understanding of a hugely-complicated issue, so it's tempting to seize on a snappy meme that happens to fit into your existing prejudices. But it's all right to just say "I don't know" now and then, you know?