You're a lot closer than most to summarising the situation. I wouldn't say it's as much that corporations think that radical progressives are the majority as that they think they can try to mollify the left's distaste for them by superficial pandering that doesn't actually get in the way of their profits. The far right's moaning about "cultural Marxism" often completely misses the point because "woke" media like Marvel comic films are written that way to maximise profit (by attracting a black audience with black characters, for instance), and because most of the population aren't far right spergs this is a profitable strategy. YouTube's crackdown on controversial content is a crude attempt to not drive away advertisers and included demonetisation of completely apolitical channels like The Great War - not a precisely targeted attack on the far right, though of course the YouTube staff despise them.I think the problem at hand (at least the way that I see it) is that the corporations and the bigwigs at the top have gotten extremely powerful thanks to trickle-down economics, while a significant portion of the Millennial generation and the social media woke-scolds have leaned full into communism, anarchism, and "Democratic Socialism" (not Social Democracy) that is filtered through an intersectional identity politics lens.
The real kicker is that the same corporate bigwigs that have too much power thanks to decades of trickle-down economics have also been spending the better part of this decade bending over backwards to appease the very loud vocal minority on social media (the same ones who hate capitalism) because they think the loudest voice in the room is the majority and so the media and the culture have gone to shit as a result.
So, we're in a weird situation where the 2010's West is dominated by corporatism on the economic level and left-wing identity politics on the social/cultural level. It's the closest we've gotten to the "Worst of Both Worlds" without going into full-on totalitarianism.
That being said, given how this year has been turning out, I think 2019-2020 are going to be the major turning point for the SJW cultural zeitgeist, the proverbial darkest hour before the dawn.