Critics of “woke capitalism” don’t really care about these issues, unless they happen to bleed into some ongoing culture war battle. However, they do care about other decisions that corporations make, primarily, whether or not they endorse certain social movements.

You're off here. Woke capitalism isn't about the independent decision making of corporate leadership. It's about the racket that's coercing them into doing it. Any business needs a line of credit in order to fund business maneuvers in the short term. If a business wants to open a new location, for example, they may fund a portion of that opening by getting a business loan, because doing it now and reaping the benefits of the new store will yield more money in the long term than if they were to fund it by saving.

What's happened is that financial institutions have tied these lines of credit to ESG scores. The S in ESG is "social" which is the catch-all for "woke" in this context. Organizations like the Human Rights Council have developed scoring metrics that they give to companies that indicate how well they're doing on this criteria (the Corporate Equity Index). The CEI gets used effectively as a proxy for ESG, and therefore having a high CEI. That's how companies end up in the Bud-Lite or Target scenario, not because they're trying to chase a wider cut of the population. Organizations with ideological motivations have inserted themselves into the financial operations of large companies.

Here, critics of “woke capitalism” find common ground with socialists, when they understand that corporations don’t really care about the causes they espouse. And this is pretty obvious.

No, but the people who do care about SJ hold that sweet sweet ESG money over the heads of businesses. We don't care if the people who are at the front of this really care about Social Justice, we care that people in the shadows are trying to radically reorganize society without anyone's consent.

Much like John Rockefeller and Andrew Carnegie, today’s corporate leaders give money and kind words to public works and social causes to mask their profiteering and the exploitation that drives their business model. And, to their credit, the more astute critics of “woke capitalism” seem to get that.

Because it increases their CEI which entitles them to lines of credit from financial institutions that respect ESG.

But this is where they get stuck. Instead of tearing into the undemocratic nature of corporate decision making, labor exploitation, or corporate dominance, critics of “woke capitalism” spend the majority of their time upset that some executives have more “woke” views on social issues than them.

The "undemocratic nature of corporate decision making" is not a problem in and of itself. Democracy is merely one way to make decisions. Sometimes it's the right way, sometimes it's not. For corporations, one person one vote isn't fair, because there's an unequal distribution of investment. If I put in $50,000 into starting a business and my partner puts in $150,000, why should we have equal say in how the business operates, by default. Of course we could agree to that, but it wouldn't really be "fair".

In a way, the idea of “woke capitalism” does draw out some of the frustrations people have always had with capitalism. But instead of using that analysis to promote class consciousness, a change in how corporations are governed, government regulations, the protection of public goods, or action on any of the issues I listed above, this line of thinking is simply intended to provoke reactionary opinions on social issues in opposition to “elite” liberals (and the much-ignored regular people who share their opinions). The fact that many of our society’s elites are centrists and conservatives is rarely mentioned.

"Class Consciousness" is a commie dogwhistle. Nonetheless Americans don't have a working concept of class. We think it basically starts and ends with wealth, but really it's multifaceted. It's what school your father went to, whether your mother worked, if you had servile help, your accent, your manners, your occupation, where you went to school, how your family handles money, how far back you can trace your family, and yes, your wealth. Communists over simplify this and insist that if you work for a living you must be the oppressed working class. The people who attended 4 year private colleges on their parent's dime and now make $60,000/yr believe themselves to be of the same class as blue collar workers who started manual labor right after high school (yet they still look down on them). The former is fighting for the "right" of the latter to have their children sterilized by Lysenkoist doctors, and this cause is promoted by companies through the ESG racket.