With such a law on the books you have legal standing to have a man removed from a women's facility, whether they are dressed as a woman or not. (and don't put words in my mouth - I never said such activity "worries me so much" - it is far, far down the list of things that worry me) Without such a law, predators and deviants might be emboldened to enter when before they would not have.
As for your second question, you first have to decide whether it is actually a civil right as a man, for instance, who believes he is actually a woman to be able to use facilities heretofore reserved for women. I think it is a civil right to be free from employment or housing discrimination due to gender identity, for instance - but using a bathroom or changing facility? I am not sure.
