Don't take this as sound legal advice, but I was a manager for four years and had to take classes on hiring practices and United States civil rights laws as they relate to hiring.
First, your comment about requiring a woman for a position: This is against the law,
unless it's a genuine qualification for the job. The classic example of where this is the case is Hooters. They were sued by a man who wanted to serve tables and claimed that he was discriminated against based on his sex, but Hooters won the case because they were able to argue that being a woman is a bona fide qualification for serving tables at Hooters. (I think we all know why.) Jobs where being a woman is a genuine qualification are few and far between, and I'm almost positive that Cato and Claire's can't make a case for this.
Sex is an example of what's called a "protected class," and that's why it's illegal to discriminate on that basis. Unfortunately, being <not allowed> is
not a federally protected class, and unless the city or state you live in or the company you're applying to specifically protects <not allowed> individuals, they're within their legal rights to discriminate against you. (Whether they're within their
moral rights is another matter, but sadly that doesn't hold any weight.)
And again, this isn't legitimate legal advice, just something I picked up at my last job.
Edit: I found a list of United States jurisdictions with anti-discrimination policies that include transgender individuals. It's available here:
http://transgenderlaw.org/ndlaws/index.htm. It looks like I'll be moving to Illinois soon.

Edit 2: Further research reveals that Hooters
lost the case I mentioned above. Oops.
