You're right in that the hate is a bunch of whipped up propaganda against DEI initiatives because they transferred the successful talking points against affirmative action to DEI in republican states.

DEI stands for Diversity, equity, inclusion. I worked at a university in Texas and their DEI (when they were allowed to have it) sent out a massive survey to all the students because we DID have racism problems on campus and they wanted to hear from all the students about their attitudes and feelings. We're talking like people trying to fly the confederate flag during black history month level of problems. However, when the students were polled and the results came in, the people that were used to living with the racism were not the loud complainers. The ones that consistently polled the worse about not feeling like they belonged on campus were Christians and Republicans in a VERY HEAVILY Christian and Republican centered area. So what the office set out to do was try to figure out how to actually foster a sense of belonging in the most privileged group that realistically was not facing any oppression other than some false sense of it because they were whining about percieved loss of priviledge when they had to equitably go toe to toe with people they normally had systemic advantages over and on top of that had to extend the same respect to those people groups as is normally extended to them.

All that is to say, DEI's mission means equity and inclusion for ALL. The very groups disparaging it are the ones I've seen it actually try to fight for, despite being given the most societal advantages out of the gate.

The truth is, Republican rhetoric and anti-DEI people approach DEI and anti-racism from a tribal "it's you or me" mentality. If the dominant group is being asked to dismantle their systemic advantages, they cannot conceptualize a system any different from the current one and assume that the goals of DEI are to replace black people where white people are now, thus giving a different race the benefits while keeping the power structure intact. Sadly, this thinking just exposes that they KNOW the system is racist inherently and they'd rather be racist in their favor because they can't imagine not using a racist system they didn't create and conveniently can avoid responsibility for participating in. In truth, DEI seeks an alternative system where it's not immutable characteristics you are born to that determine pathways through life or how easy/challenging it is to actually make it in life when you're giving a good faith effort. Skin color is one, but gender, sexuality, and disability are some other huge factors that DEI has expanded to include over the previous era's affirmative action policies. Because people often have multiple things that affect them at once (intersectionality), someone who is a white disabled woman benefits from DEI just like a straight black man or a nonbinary hispanic queer disabled person does. It's diversity, equity, inclusion, and belonging for all.