What will happen more than it ever has is men will start looking like woman and woman will start looking like men. They're competing against each other. But moreso, we'll start seeing people who don't look like men or woman.
What we're seeing is the relaxing of conservation of energy (maybe you might call it natural selection or natural evolutionary pressures). This will result in very diverse genetics. Don't be surprised if people start sprouting wings or feathers or something weird like that. Don't worry. Technology will allow us to change our genes anyway. Nature won't have much say anymore. Same deal with the planet. We're going to engineer the planet or become extinct in the attempt.
Ultimately we'll produce children in labs. Why? Because it's too much risk to hand over a child to nature. It's like throwing a child into the jungle. Once we can control it, we'll control it. Someday we might not be biological anymore.
They call it equality. In reality it's the relaxation of natural pressures:
https://www.youtube.com/watch?v=Ue-EsVSDiGQ
Make no mistake: I'm not against this. It's just physics. There's nothing we can do about it. In fact, if we try to stop it or turn back the clock we'll actually hurt ourselves. We're conserving energy, so it's good.
EDIT: Some forum goers might not have read my other post. You might wonder what I mean by conserving energy? Well it's simple. A man doesn't need to be a muscular machine anymore. Machines do that now. Woman don't need to cook because the man can do it just as easily and if nobody wants to do it then they can just grab premade meals from the freezer. The list goes on and on and on. Husband and wife don't need to parent as much because of schools, day care centers and other economic developments. Woman don't need to be woman and men don't need to be men. It's wasting energy trying to be a man or trying to be a woman. Instead we're choosing to diversify and seek out more efficient uses of energy.
Crossover is when a female has male traits or a male has female traits. Because we're seeking to diversify and use our energy more resourcefully, crossover is being sought and encouraged. So we're going to see more and more of it. Like I already said, this is the tip of the iceberg. Consequently, we're going to see new gene configurations which're not male or female (or human).