First, someone identifies an opportunity to improve diversity, equity, or inclusion in some way. DEI statements in academia, codes of conduct in open source projects, some rules around topics or specific language on a social media site, I'm sure you can name some other examples.
Now, this new thing may be a way to address the problem, or not. The problem it's trying to address might have been well understood or not. One way or another the idea gets some momentum.
Next, bigots get wind of the thing and start concern trolling and spreading FUD about it. Everything they say is carefully crafted with a veneer of respectability and plausibility. Any accusations are re-directed. There are people who are motivated and very skilled at making plausible sounding bad-faith arguments. The plausibility of course also convinces people might not intend to be making a bad faith argument, and so are authentic in their indignant responses to accusations of acting in bad faith. Still, the entire point of the arguments was ultimately to disrupt efforts to improve diversity, equity, and inclusion, and to uphold inequality. In some cases these bad faith arguments can end up being a vast majority of the discussion. They make up maybe 80% (not an exact figure) of the comments in any given HN thread about anything tangentially related to DEI for example.
The people trying to make a positive change who have been at it for a while are generally exhausted with trying to deal with the torrent of bad faith arguments, quickly recognize the pattern of them, and ultimately often end up serving as fuel for further bad-faith arguments.
In the end, it becomes nearly impossible to have a productive good faith discussion about whether the original idea is good or not, or how to improve it, because nobody can disentangle legitimate contributors and arguments from the torrent of bad faith actors who are ultimately just trying to disrupt the process. Meanwhile, communities that ought to be served by the initiative are often left standing around watching their value as people or rights to participate equally being thrown around as an abstract subject of ideological argument.
Without any better options, people double down on the original idea because it was at least made in good faith.
It might sound like all of that is an argument against DEI statements- after all, I just spent several paragraphs talking about why it would be hard to have a reasonable good faith debate about it. Still, I think that in this situation they serve a couple of useful purposes. First, I think that it moves discussions around concrete improvements away from a forum where they can be undermined by bad faith arguments and toward a form where individual authors of DEI statements can focus on concrete actions. It incentivizes action over getting mired in these bad faith arguments. If one is to write specifically about how they have or will work to improve DEI, then they necessarily must move past the bad faith and concern trolling arguments and pick some specific actions. Second, I think that it acts as a useful honeypot for people who simply can't act in good faith. If you can't identify any dimension at all along which you will work to improve DEI for any group, then it's hard to see how you can further that part of the mission of an organization. Finally, while it is virtue signaling, that doesn't necessarily need to be bad.