I watched a semi-popular movie called deadpool, in which the "hero" comes across this dilemma while fighting female assassins, and we are not shown the results of his introspection. Here is the problem as I see it:
Men fighting women. Then you have to deal with inter-gender violence. "Your good guy is hitting a woman!" Women fighting only women, and possibly the slimiest and most evil of men. Then you have to deal with inequality - "what, women aren't good enough to fight alongside men?" Women don't fight or get hurt. Then you have to deal with lack of representation. "What, women aren't important enough to be given an important role?"
Say the story revolves around a female villain who is a pretty significant threat. Not in the way of Catherine tranell, a character who is dangerous in the way a femme fatale is, but can kill you through magic or some other kind of power. Things will have to get physical at some point between her and the male hero. How would you write that? Would you find it cringy?