They want people to punch down, blame the person scraping by on welfare or the person who's identity is maligned for what is actually caused by massive wealth disparity. MLK Jr didn't advocate fighting a vague notion of racism, he convinced black and white unions they were stronger together and that economic equality as a class program was the mechanism to combat the issue, with specific laws and legislation and job action as the tools available. In a certain context, the biggest advocacy group for the rights of gender non-conforming individuals in the world right now is the AFL-CIO.

Definitely agree and I think sometimes people conflate intersectionality with the way it's been commodified and adopted by capital and it causes debates because it's not precise about what the problem is. A lot of left scholars have been a lot more pointed about the "problem with diversity" not being about "diversity" or inclusion etc. It's just important to recognize why it doesn't threaten capitalist institutions, which doesn't mean it's bad, it means it's ineffective for that purpose, it's like being nice to people at work. Education on intersectionality that a lot of people are exposed to is often mediated/coerced by employers through business relationships with HR/diversity industry consultants. They're presenting very specific notions of the topic that they're able to sell to employers, and employers are being sold on it as basically a branding/marketing thing to "make the company look good," but leadership might even be personally invested in it and genuinely want people to feel included at their company, it's not a radical notion at all. The problem is the inherent conflict between employers and employees and how it dictates what notions of intersectionality or EDI are presented in that context.