I get that this makes some people uncomfortable, I do. But that is still their discomfort. They need to deal with it. Just as people need to deal with discomfort over so many other things, such as having people breastfeeding in public or even having those of the same sex either naked in front of them or seeing them get naked. Plus, what about the men who would feel uncomfortable with a transgender woman in their locker room? Their feelings of discomfort aren't important? Why wouldn't women also feel uncomfortable with this "woman" around them in places like the restroom or locker room?
10 Handsome Men (Who Were Born Female) (transgender female to male, female to male transformation) - ODDEE
Or any of these guys really, because that is what women would see them as, men, despite their being transgendered/transsexual men, meaning they were born as women and would be viewed as "women" to many arguing "you can't change what you are born as".
Simply repeating "well they are a man or woman physically", really isn't an argument. It doesn't get down to why they need that label and why that label can't be changed, let alone what that label is really based on. There are plenty of ways to describe a "woman" or a "man" biologically, and then plenty of ways to completely defeat that definition with what happens in real life. And when people almost always judge gender by appearance, usually how a person is dressed, presents themself, then it shows that gender is not really dependent on those physical characteristics. Sex might be for most, but gender would deal with how we refer to people, "yes ma'am", "no sir", she, he, her, him, etc.
"A woman is like a teabag, you never know how strong she is until she gets in hot water." - Eleanor Roosevelt
Keep your religion out of other people's marriages.