From what the trans people I'm in contact with (most of whom are trans women) have been saying, automatically placing trans people into a third category separate from men and women perpetuates the notion that trans men and women are not "real" men and women. Trans women and trans men have spoken a great deal about the harm that this does.
Of course, people who don't fit neatly into the categories of "man" and "woman" do exist: intersex people, third gender people, genderqueer people, non-gendered people, and so on. Even so, trans men and trans women have been very clear about the fact that trans women are women and trans men are men. See the links at the end of this post for more resources.
All that said, the "men, women, and trans people" phrasing raises important questions about how we discuss gender in theatre and what it is we're working for when we say we're working for gender parity.
Questions like: How do we make it clear that, when we speak about gender parity in theatre, we are including trans women when we talk about women? How do we include other gender minorities when talking about gender parity in theatre? Is the gender problem in theatre about the dominance of men in general or the dominance of cisgender men in particular?
As with any questions addressing the systemic and structural elements of marginalization, I don't believe there are simple answers to these questions. But I'd love to hear from trans people about needs to happen in discussions about gender parity in theatre.
And now, some resources about gender identity and transgender people.
I have no time to rehash information that's readily available via a Google search for "trans 101." Here are a few links to get you started. Any further investigation, which I hope you are doing, is on you.