I do want to make a point or two, however, that I think better refine the idea. It would be a comment, but I am cheap.
1: Leftism’s commodification of women, victimhood, identity, what have you, is not so much an acceptance of markets, but rather the result of the reality that markets are what humans do. That is to say, demand drives supply, one way or the other, and this is true in all things in nature. In the case of the modern American leftist follower of Wokism, what is desired is the appearance of victimhood, an identity that conveys the prestige of the oppressed, that puts one into the category of people who must be “centered”1. These categories include women, racial or ethnic minorities, the sexual alphabet crowd, trans-people, etc. and there is a definite hierarchy between them, not only based on intersectionality (how many categories can you check off) but on perceived level of oppression. Since people want the status that comes with attaining these categorical check boxes, people will figure out how to acquire them. Apparently commodifying race is right out, but the other aspects are easier or harder to acquire, and humans being humans we seek out how to acquire such things in ever more clever ways. We humans assign categories based on signals and traits, not fundamental truth, and so acquiring the symbols or traits piece meal is what we aim for.
That’s what happens, and what always happens: every marker of status is something we will figure out how to manufacture and acquire, unearned or not. Leftists like to think they are above markets, but markets are how we interact with non-family members, and so drive nearly all our behaviors.
2: Since the time of Marx, leftist beliefs have generally been luxury beliefs, in that the rich can get away with holding them but the poor cannot, or in that they benefit the rich but harm the poor if society accepts them. Communism is great for those in power who inevitably become the rich, and terrible for everyone else. Government schools are bad for everyone except those who can pay to send their kids to private schools. The Great Society in the US was awful for the poor, destroying families and institutionalizing dysfunction, while the rich who are farthest from it hardly notice. The list goes on.
That isn’t to say that the ideas of the right have been much better; bad ideas for organizing society pop up like toad stools after a long rain. In general, however, the ideas characterized as left have almost always represented a step back from reality in an attempt to get humans to act as though we are all in one family, and can solve any and all issues by application of wealth with little regard for the consequences. If that seems overly harsh, well, it should, because the Marxist strain of leftism deserves a great deal of opprobrium, although it is not a shame that belongs to the left alone. Statists often sell those ideas, and they seem perennially appealing to humans. Still, it is very difficult to think of a single leftist only policy or belief that is not in the realm of “fine if you have money, bad if you don’t.”
Dreaming of utopia is always a lot easier for those with plenty of resources than for those who have to work for a living.
For those who can’t get that identity or find it too costly, the next best option is the “Woke-scold”, the ally who crusades for the victims’ rights.
Dreaming of utopia is one big driver; the other is the desire to feel holier/more sophisticated than thou (one's middle class peers in other words). As for the harm that all this brings, I keep coming back to TS Eliot: “Half the harm that is done in this world is due to people who want to feel important. They don't mean to do harm; but the harm does not interest them........ because they are absorbed in the endless struggle to think well of themselves.”
You say "Apparently commodifying race is right out".
Unless you are a liberal white woman claiming to be Native American?