There was a recent debate on this[1] and even the debater for the pro DEI statement side (that they could find) admitted that DEI statements that were just ideological pledges were wrong, and he was only in favor of statements about concrete things you did to advance the DEI agenda (eg. "I did a, b, and c in my previous position to enhance DEI in my department"). He argued that was justified because DEI (at least the principles, not necessarily the specific policies like affirmative action or whatever) were ostensibly things that the university cares about, and therefore they were fair game to ask for.
[1] https://opentodebate.org/debate/are-dei-mandates-for-univers... (it's a podcast but there's a transcript tab on the page)