I'm not going into Transgenderism, as someone else has already touched on it (and I know only what I know about Trans people), but I'll cover the
binary system of understanding, which I have
first-hand experience with, and from a combat-sports angle.
Considering the massive biological differences between men and women, my first response to the idea of removing the barrier between men and women would simply be "No." or "Have you considered the problems that could arise?" My reasoning for this position are not complex, but I'll try to explain deeper, with as few words as is feasible.
I'm biased, but I will admit that on the surface, removing separation of the sexes sounds like a great idea, and a progressive one at that, as it would allow for
equity among the sexes, but I do not believe it would create
equality. Rather, it may cause more problems, such as actual sexism within the sport (on and off the field). If men and women could be trained to be absolutely devoid of our natural instincts, I might be inclined to say different, but short of a
miracle in our evolutionary history-to-be, I don't think it could be so.
I, for one, could emotionally separate myself from my actions in a single-gender combat sport situation, but I feel like I would end up going easier on a female opponent, or she may do likewise--which is an insult in
any combat sport, especially when it's against guys. While I cannot claim to know what might happen, and it would certainly be interesting to have an equitable faceoff with a woman in combat, I don't think I could get into the octagon or in the ring without viewing her as someone I should be ashamed of myself for hurting, or someone I'm failing to protect by engaging in boxing, BJJ or kickboxing. It's my opinion that Men and Women need separation in the combat sports area, at the very least. If we don't do that, women like Holly Holm, Michelle Waterson ("The Karate Hottie") or the absolutely amazing Rhonda Rousey would literally be pushed aside, out of any potential spotlight--and that wouldn't be fair, even in a sport like MMA, which doesn't typically deal in special treatment to begin with, short of regimens. That would be the downside of gender integration in this sport, in my admittedly limited scope of understanding.
I hope that was as precisely worded and coherent as I intended it to sound, and answered your question satisfactorily.
(Equity and Equality are two separate words, meaning two separate things, and I don't mind going into that upon request)