I agree that argument is stupid, but while nobody in this thread has argued for it, it's certainly been argued for by posters on this board in other threads. Even stranger definitions of racism have been argued for. I no longer remember the details but something like 'racism is believing race is real'.
But if they're not part of the current discussion, then you're not arguing against anyone's points by bringing them up.
Words get redefined and meanings change all the time. Arguing that one redefinition is silly isn't an argument against a different redefinition. The redefinition of racism to only apply to whites was a nonstarter because so much meaning of the word was lost in using it that way and it introduced a whole lot of confusion about what it was that the person was saying. Redefining racism to mean general bigotry does not, since doing so does not sacrifice any meaning in the phrase and there's no confusion about what's being said.
The phrase "he's racist against women", while grammatically incorrect, keeps it perfectly clear what the person is saying, which is why it's becoming less and less grammatically incorrect. That makes it not comparable to a phrase such as "black people can't be racist". Just like bigot now refers to non-religious matters, despite the derivation of the word literally being "by god", racism is simply a word which is getting a broader definition without sacrificing any meaning.