The mathematician in the article disagrees with you: "Thompson, a mathematics professor at UC Davis, spoke approvingly of DEI efforts at large, but criticized mandatory DEI statements and compared them to the loyalty oaths of the 1950s."

The California loyalty oath is from the 1950s, and required of every state university professor.

The fact you see DEI as "specific ideology" is because it's been hyped as a culture war bogeyman.

The so-called ideology is something like "gender, race, and socioeconomic status influence training opportunities and outcomes. The university hopes to be a more egalitarian and just place of learning for the entire student body, so candidates are expected to acknowledge the issue and show how they plan to address and improve the matter.", right?

That ideology is little different than "the university is primarily a teaching university. Candidates must demonstrate how they plan to include students in their research, with examples from previous employment, if applicable" or "the university believes in maintaining strong ties with the local community. Candidates must include plans for how they plan to engage in outreach as part of their service obligations."

Or, "20% of our student population are first-generation Native American students. As a land-grant university on lands confiscated from their ancestors, the university feels a special obligation to ensure Native students have the same ability to get a good education as our other students. Candidates are expected to show they understand the relevant history related to American colonialism, the Indian school system, and discrimination against Natives, and demonstrate how their lessons will be aligned to the university mission."

Or, "The university was founded as school for the deaf, and while that is no longer a requirement for enrollment, fully 60% of our student population are deaf or hard-of-hearing, which we feel shows our continued dedication to the deaf community. In your application, please highlight any experience in working with deaf and hard-of-hearing people and how your teaching plans will take their needs into consideration."

All those are ideologies too, right? But that doesn't make in bad, or even suspect, because ideologies are everywhere.

Capitalism is an ideology. Adherence to the hierarchical structure of most companies is also an ideology. Democracy is an ideology. Civil rights is an ideology. Political party membership is an ideology.

That you don't see the ideologies in your workplace mostly means you are like the proverbial fish unable to perceive the water it floats in. Even "I have read the employee handbook and agree to follow it" is forced ideology - don't agree to it and you can be fired.

Given how many people make exactly the same Soviet Nomenklatura comparison you make about DEI, where is great outcry against religious schools in the US which require their teachers have specific ideological stances, like how a Catholic school can require the teachers be Catholic? Where is the great outcry against the California loyalty oath?

No, it's a bogeyman, causing people tp look for any possible argument to scare it away, even if the argument is inconsistent with everything else they believe.

And, "DEI priesthood"?! Do you also see communists hiding under every table? Because that's what you sound like.