There are times when someone wants to cause pain to another, and chooses a response to inflict maximum harm. This could be a racial slur, but it could also refer to a death of a loved one or something else. Imagine someone telling another "I see why your son killed himself." It is meant to cause maximum damage, not meant to be racist/sexist/etc.

In these cases, I don't think there should be any difference in forgiveness between those who used discriminatory language and those who picked another means to attack. I'm not saying people should accept a sincere apology. I see such an attack as very bad regardless if it used discriminatory language. The intent, to cause maximum pain, is unjustifiable regardless of the tool used to carry it out.