If in some alternate universe primates of all types had evolved to have white fur, like polar bears, and humans all had the pale coral, beige-ish skin that is, in this universe, typical of humans whose ancestors settled in northerly climates...
humans would still compare other people's behaviour to that of chimpanzees, just as I have mentioned my MIL's cat. The same would also happen if all humans had pale skin and all other primates had black fur, golden fur or red fur.
We don't live in that universe, so I avoid ever using primate comparisons in face-to-face conversation in case I accidentally slip up and use it to a black child. Why? Because they could justifiably conclude it was a racial reference. It would be an entirely reasonable misunderstanding, so I take care to avoid that.
However, I cannot agree that online text-based conversation where we respond to what other people have typed is the same as real life.
I absolutely cannot agree that it is always a racially-charged term and this idea that an ape comparison actually means the speaker is comparing you to a black person is so out-there I can't believe it. There is something very insiduously nasty about that chain of reasoning, and it sounds about as racist as throwing bananas at football players.