Yes, because it's so obviously racist to treat people equally regardless of their "race". We must all strive to judge people not by the content of their character but by the colour of their skin - that's equality there.
You seem to be confusing treating people equally with treating people the same.
Comparing black people to monkeys is highly offensive due to history so you don't do it, full stop.
I also had Asian friends who would use the term "coconut" as an insult to other Asians, they explained it as a slur that meant brown on the outside but white inside. Again that is highly offensive to a certain demographic, but not so much to me as a white person.
If there were a term that was used derogatorily towards me being white I would not want people to use that.
So we treat people differently in that we don't use certain terms as it is offensive to them specifically, but we treat all people equally by not using offensive descriptions.