No, the issue is not that trans people harass or assault people more, it is that a law that says people can change clothes in whichever facility they want will allow non-trans people to hang out with, observe, whatever, people of the opposite sex. AND, DESPITE WHAT YOU APPARENTLY THINK, YELLING DOESN"T MAKE YOU SMARTER. Of course there are laws that deal with assault and harassment - no shit. Once the law allows a man in the women's locker room, what law will allow him to be kicked out because he is just hanging out in there casually watching the women?
Maybe the net result of all this is that we go to single stall bathrooms and locker rooms with more private, closed-off spaces for changing.... Then perhaps it won't be as big a deal. I just know that the locker rooms I have used in the past, and use currently, are mostly open spaces with naked dudes walking around, toweling off, changing clothes, etc. It doesn't seem like the ideal place for gender-mixing...