The nominal case doesn't always match the reality, but the reality is that no one has a level playing field to begin with.
In theory if DEI was about being race, sex, gender, sexuality, age blind, it wouldn't be controversial.
But companies went in hard with things such as quotas, and there's even cases in the courts at the moment where Red Hat/IBM supposedly awarded bonuses based on hiring managers fulfilling diversity quotas.
I think it would, there is a substantial contingent that wouldn't even like that.
And that's only those who directly materially lose out. Implicit in DEI is a suggestion that the American system is not a meritocracy, and if you accept that claim you are attacking the identity of a lot of powerful people who genuinely believe they got to where they are through unique skills and effort and not because they had any sort of advantage.
I think there are also some other types of policies (whether formal or informal) that were much more controversial. For example: https://www.seattletimes.com/business/lawsuit-claims-google-...
The reason is that de facto unofficial discrimination against white men is widespread and blind screening eliminates it, so the resulting hires are more male and western than before. Mostly this result is kept hidden within the organizations in question, but there are a bunch of reported cases where this happened publicly.
Even the famous orchestra study that kicked off the fad for these screenings supports this if you read the data tables carefully. The paper made it sound like blind screenings are better for women and racial minorities, but their data properly interpreted didn't say that.