I'm looking for a word that describes SJW, feminist people or others who judge entertainment, political or social topics by race and diversity. Note: I was thinking about the word racist but that implies hatred towards a race
The suffix "-centric" is defined in Oxford Dictionary of English as
forming an opinion or evaluation originating from a specified viewpoint
An example for this is Eurocentric, defined as
focusing on European culture or history to the exclusion of a wider view of the world; implicitly regarding European culture as preeminent.
Replace "Europe" with "race" and perhaps "race-centric" would best describe someone whose viewpoint originates or revolves around race. This is an adjective, not a noun like "racist," (at least for the moment) but you might find it useful.
I initially dismissed this, remembering it only as a British synonym for racist, but I looked it up and it fits the bill:
Racialism a. An emphasis on race or racial considerations, as in determining policy or interpreting events. b. Policy or practice based on racial considerations.
The word you are looking for is racialist.