I fail to see the relevance of that point. Are you implying that gender-specific insults should be off-limits because gender-specific insults are hate speech? That it is the gender-specific quality of a curse word which puts it past a bright line? I don’t agree, but I would be interested in hearing the argument supporting that premise.
It’s a complicated question but I’m going to say no, calling a black man who punches your wife a nigger is not hate speech just because you called a black man a nigger. It could be hate speech if you show hatred towards a class of people, but I am of the opinion that the word “nigger” alone does not do so. Not even when used as an insult or ethnic slur.
I’m probably on my own with that opinion, but hey, I read replies with an open mind.
~Max