whether it's a good description of their activities

Sure. (Actually, I think there is an important difference between a movement that says, in so many words, "throw away everything old and traditional" and one that isn't willing to be explicit about that. But I'm happy to leave that aside.) And the way it looks to me is not that the SJ movement wants to be rid of classical literature and traditional festivities, but that it wants classical literature taught, and traditional festivities celebrated, in ways that don't upset certain groups in certain ways.

Maybe that's a great idea, maybe it's a terrible one. But it's a long way from saying "out with everything that's old". The sort of "cultural appropriation" some university groups were complaining about at Halloween are actually a relatively new thing. Actual traditional Halloween has ghosts and skeletons and witches and the like, not people dressing up as Mexicans or putting on blackface. And slapping "trigger warnings" on the rapes in Ovid's Metamorphoses might be a waste of time, or might be overindulging people you would prefer not to indulge (though, for my part, I incline towards being generous with accommodations for rape victims) but it doesn't erase Ovid from the canon or stop anyone reading his poetry.

Surely there must be a point at which we have to conclude that this movement [...] is leaning all-the-more towards a largely futile quest to remake [culture] from the ground up.

Surely. But I don't see anything suggesting that we've reached that point, or that we're going to.

even the cultural revolutionnaires were somewhat limited in their effects

They were, but they got a damn sight further than the SJ movement has. I don't know how far that's because they were genuinely more extreme, and how far it's because they had the might of a totalitarian state backing them up -- but it's because they did so much damage that the Cultural Revolution has the deservedly terrible reputation it has. Just by way of reminder, here are a few examples (taken, because I am lazy, from Wikipedia):

Historical sites in every part of the country were ransacked and destroyed. [...] Beijing [...] where thousands of designated sites of historical interest were destroyed. [...]

Red Guards from Beijing Normal University desecrated and badly damaged the burial place of Confucius himself and numerous other historically significant tombs and artifacts. [...]

Libraries full of historical and foreign texts were destroyed; books were burned. Temples, churches, mosques, monasteries, and cemeteries were closed down and sometimes converted to other uses, looted, and destroyed. [...] Clergy were arrested and sent to camps; many Tibetan Buddhists were forced to participate in the destruction of their monasteries at gunpoint. [...]

Public security in China deteriorated rapidly as a result of central officials lifting restraints on violent behavior. Xie Fuzhi, the national police chief, said it was "no big deal" if Red Guards were beating "bad people" to death.

In the course of about two weeks, the violence left some one hundred teachers, school officials, and educated cadres dead in Beijing's western district alone. The number injured was "too large to be calculated." [...]

In August and September 1966, there were 1,772 people murdered in Beijing alone. In Shanghai there were 704 suicides and 534 deaths related to the Cultural Revolution in September. In Wuhan there were 62 suicides and 32 murders during the same period.

So I'll tell you what. When the SJ movement has destroyed one major historical site and murdered one person, get back to me and I'll willingly agree that the SJ movement, having done only three orders of magnitude less damage than the Cultural Revolution, can reasonably be put in the same pigeonhole for some purposes. Until then, I'm quite comfortable not summoning up the spectre of Mao to haunt us as we watch a few overzealous student societies asking for trigger warnings on classical literature.