Lets compare to a similar situation but without this being about men vs women. Two co-workers go to a bar, and gets into a physical fight. During the fight, one of them call the other something really inappropriate like n__gger or s_ut.

Do you fire both instantly the next day? Physical fights and insults are both unprofessional, and as a zero tolerance policy, that means they need to be let go instantly. Do you only fire the insult throwing employee? Do you talk to either one of them before issuing the boot?