Equality: that I should have as good of a chance, by law, to succeed or fail in any particular enterprise, as someone else.
In pretty much any other way, we are not equals. We do not need to be equals. We should not be equals.
We are what we are. Where there is a genius, there's a retarded kid. We should not be so separated, mentally (and spiritually, but that isn't going to get better any time soon, by the looks of things), that a person feels envious of another, threatened by another, or sorry for another.
Each of us can do what it is our will to do, and should not be dissuaded from that. OTOH, some people like power. Others come to feel safe with fear. Much of this is nothing but knee-jerk reactions to keep one's mind feeling like they are safe. Both religion links are mostly this.
Some things, though, such as the locker rooms, are simply common sense. It'd be nice to live in a world where people didn't think twice about it--after all, if everyone was emotionally supported and moderately level-headed, what would be the harm in combined locker rooms--but the reality we are in is not that world. In this world, we can be assured that someone would be stupid.