Can We Save Universalism from the Culture Wars?

I'm going to talk about "woke" and "wokism". And I'm going to do it as a privileged person: on the Wheel of Privilege and Power (if you're unfamiliar with this concept, here you can find more information), I'm quite near the center, or at least in the middle section.
But perhaps the real difficulty in talking about wokeness is that there is no such thing as a singular "woke", because this word has many different, and sometimes opposing, meanings. It's an "umbrella term", as it's often called: a word that covers many concepts and ideas not necessarily related, like an umbrella that covers me, the groceries I've bought, and my backpack.
In particular, "woke" is often used as a catch-all term to identify everything and everyone we don't like. In particular, "woke" is what doesn't fit into an imaginary traditional society that we can approximately locate at the end of the 19th and beginning of the 20th century. A society where men were men, women were women, LGBTQ+ people didn't exist (or accepted their "unnatural" nature), marginalized people didn't complain, et cetera, et cetera.
Given this definition – where 'woke' simply means rejecting an imaginary traditional society of rigid roles and exclusions – I have no choice but to embrace being woke. I unquestionably prefer a society where everyone is as free as possible to find their place while resisting imposed social obligations.
But that's not the only "woke" in town. Next to the social movement that asks for a society where everyone is welcome and demands vigilance against all forms of injustice and discrimination, there is the "woke ideology". And again, while "ideology" is often used as a derogatory term, by "ideology" I mean the philosophical framework of an idea. And here it becomes difficult for me to consider myself "woke". There are of course many other flavors of woke, one of which is particularly disturbing to me: "woke capitalism", where diversity and inclusion are instrumentalized to increase profits without any genuine interest in social change. This is a degeneration that I hope no one will defend.
What follows is a personal reasoning, but it's important to highlight three books that played a role in developing my opinion. Two of them are recent essays that address wokism directly: The Identity Trap by Yascha Mounk and Left Is Not Woke by Susan Neiman. The third one apparently addresses another topic: In Defence of the Enlightenment by Tzvetan Todorov. I also want to cite an issue of Massimo Pigliucci's newsletter about the Enlightenment – which, as you've probably guessed, is central to my argument.