Do I think men with dicks, dressed in women's clothing, should be allowed to share locker rooms with women? No, I don't. As long as a man has his biological sex, he is still a man, and most likely with the same set of hormones, reactions and abilities like other men. Now, before you boo me out, consider the opposite. Are women, dressed in men's clothing, allowed to be sharing locker-room with men?
Gender equality is not based on sexuality, but a view on men and women as equally worth. Equally worth but not the same. I've taken a class in Gender science at Malmo University, my mother was an Equality Ombudsman for a union in Sweden, and my father has been fighting for girls' rights to go to school in Afghanistan. Thus, we spoke a lot about equality in my family, and I see myself as a very accepting and liberal woman, but perhaps differently then what you think. I don't care what people wear, regardless of sex. But as far as I know, it still is mostly men who rape women, or other men. Should women not feel safe in locker-rooms just because some men want to wear lipstick and short skirts? And also the opposite. I know of a male gay dance teacher, who once was fondled by a woman inside the women's locker room. That too is not ok.
Rather than looking for similarities, or worse, trying to make us into the same, we should embrace our differences and see how these can contribute to a better world, where our diversity is the actual contribution.
My grandfather, who was a fire-chief in uniform his whole life, once told me that the reason why not so many women work as firefighters, was not at all due to some skewed view, but the fact that women tend to have smaller lungs and thus smaller capacities. Hence, they can't withstand the smoke and the oxygen masks as well as men. The same very grandfather, remarried when my parents got engaged, to a German woman that I've always seen as and loved as my grandmother. She was mostly a homemaker and had only a small pension with her. Yet, my grandfather used to pay her a monthly salary, out of his own, for her to feel that her work at home was valuable and equally worth.
It's all about worth. To get paid the same for the same job. The last advertising agency I was full time employed at in Sweden in the late 90's, paid a younger man, with less education and experience, 500 USD more per month for a permanent position as a junior Art Director, while I, who was hired as a Copywriter (not junior) and with the best education in Sweden, where I was part of the team selected as the best exam project of the year, got a temporary position, no car, and less pay. This was one of many reasons, why my boss and I both agreed upon my termination some 6 months later. My only regret about it, was not following my intuition rather than others' reasoning, to not even take that job offer.
When we learn to develop a true sense of respect and appreciation, we won't even need any discrimination laws.