What the fuck is an "equality of outcome" with regard to locker rooms?
Again, I will stress the point, no one is required to undress in front of anyone else. This seems to get lost in your analysis.
If negative impacts were a real thing in this discussion, we would have to account for all those men and women who will not disrobe in the presence of the same sex. They avoid the locker room for the same reason as those who do not want a transgender person to see them naked. No one is arguing for them. Why is it suddenly and issue when a transgender person appears?
Don't you think that someone who would prefer to shower at the gym but doesn't because they don't want a person of the opposite sex gazing at their genitals has suffered some harm?
If we determined that if lockerrooms were co-ed women would be far more likely to suffer this harm than men wouldn't the "go home and shower if you don't like it" policy you espouse be a policy with disparate impact?
This is not an entirely new concept as we have been debating "potty parity laws" in our society for decades now. One would think allocating equal floor space to men and women would be "equality", but it turns out women get allocated a lot more in most legal systems:
Current laws in the United Kingdom require a 1:1 female–male ratio of restroom space in public buildings.[12] The International Building Code requires a 2:1[citation needed] female–male ratio of toilets.[13] New York City Council passed a law in 2005 requiring this in all public buildings.[13][14] An advisory ruling had been passed in 2003.[14] U.S. state laws vary between 1:1, 3:2, and 2:1 ratios.[1] The Uniform Plumbing Code specifies a 4:1 ratio in movie theaters.[1]
http://en.wikipedia.org/wiki/Potty_parity
Would you take us back to the era where private enterprises could simply make whatever choices they want about their facilities, and if people don't like the outcomes they can suck it?