"Illogical" was a bad choice of words on my part. Both things (white people not caring about actual racism because they hear things called racist too much in situations where it's ambiguous, and black people calling out things as racist without significant evidence) are illogical.
My point is that one of these illogical things is born out of living your entire life seeing people of your race, for no reason other than their race and the fact that they were born in America, live in destitute, seemingly hopeless conditions. Seeing black people functionally quarantined into war zones, with terrible schools with low budgets, few options for healthy diet, fewer job prospects even for those with equivalent credentials to a white counterpart, profiling by police leading to a higher rate of incarceration of blacks irrespective of actual crime rates, harsher sentencing for the same crimes, being followed constantly at stores, being treated different in general by many people (and by "different" I don't mean treated wrongly, I'd actually say most people do not treat blacks disrespectfully the majority of the time, but there is certainly an undertone of reservedness and sometimes possible fear from thinking of blacks as "outsiders")
Blacks are reminded of this kind of stuff constantly. Constantly. They live their lives being reminded of racism (explicit or implicit) at every turn. This is why I tend to find hasty proclamations of "racism!" pretty understandable. If you see racism constantly, and it is negatively affecting your life constantly, then paranoia is bound to result.
The second illogical thing is linked to the first precisely because it is born out of not truly understanding all the stuff I wrote up there ^^^, or not having very much empathy. Is there a lot of "noise" with black people claiming things to be racist that might not have actual racist intentions? Perhaps. But most racism is not explicit and uniquely identifiable as racially motivated, and yet somehow black people are generally born second class citizens. Instead of taking great offense to understandable paranoia about racism, people should take that paranoia as a signal that something is incredibly, incredibly wrong.