That term was in common use a generation ago and for someone like Ken, it's reasonable that he wouldn't be knowledgeable about how the term is perceived these days and what other terms are more acceptable to black Americans. Alexander explained the situation to him and along with BB's warning, it feels like a fair response.
It seems that Ken is deliberately trying to be controversial and provocative in order to get evicted first. Fair enough - lots of other CBB housemates have attempted that - but Ken seems to have gone too far, from a pantomime villain into a genuinely horrible person.