It's been my experience that most of the men that are really against women fighting are either insecure, ignorant, have never seen a high-level womens fight, or are just sexist and nothing you can do could change their opinion.
The reality is that people are not interested in watching women engage in conatact sport. Doesn't matter if it is football, ice hockey, boxing, or mma. There are plenty of women who play ice hockey well but good luck finding anyone to watch a game. Bottom line is that this is all provided for entertainment and people are not entertained by women hitting each other in any medium.