Well, people certainly aren't ever going to get over their weird biases about how to play around the other gender if they never play around the other gender. It's something that would change with time.
I am well aware of the physical differences between men and women, but I wonder how much the gap can be bridged and how much a sense of place is involved in peoples' performance. Part of what gives me this idea is the hyperbole in the Olympics. Athletes so consistently get better with each games that it makes me wonder how much a person's physical abilities are based on the standard that is set for them. Many records now would have seemed ludicrous 50 years ago, but it's the result of each generation having no motivation other than the do better than the previous (it's worth noting that there are cases where the current womens' record beats a men's record from the past). It makes me wonder how much a competitive woman who may also receive enormous financial rewards could measure up to male athletes.