Transgenders should certainly be allowed to use the ladies washroom, especially those who like to recognize themselves as a woman. The issue of gender recognition when it comes transgenders sparks quite a lot of interesting debates. While most people say that gender is based on the body orientation, others argue that gender has nothing to do with the body rather with the mind alone.
In the case of transgenders, it seems like they should be allowed to enter the ladies washroom primarily because there is no transgender washroom in the first place. Secondly, since most transgenders recognize themselves as females, it is just plain justice to not to stop them from doing so.