Yes, the statement is confusing, as I mentioned. Geiger later clarified that she meant that she will not serve transgender people in her shop, but that's not obvious from her initial post.

To directly answer your question, transgender people usually identify as either man or woman, though non-binary people (who count as trans) variously identify as genderfluid or third gender. Third gender is an ancient human gender identity seen in many cultures, for example the Hejira of South Asia and the Two Spirits of some North American indigenous cultures.