I’m not a scholar, but I think I’m pretty close to the fringe liberals on “critical race theory”, and nowhere that I see does it call for stifling debate or suppressing speech. Rather, it makes very pointed criticisms of much of the conventional wisdom of both conservatives and liberals, and sometimes that criticism is made very harshly. But CRT doesn’t call for or condone threats or other things that can stifle speech, AFAICT.
I still hold that most of this consternation comes about because so many of the wealthy, powerful, and influential aren’t used to harsh and pointed pushback and criticism. When privilege is what one is used to, parity/equality might feel like oppression, and criticism might feel like attempted suppression.