I think you can not be Transphobic without supporting every single aspect of Trans rights, particularly when there are issues to hammer out.

I don't think one is dependent on another.

Some women do not support feminist push for equal pay or trying to get men to do more at home. Yet they are still recognized as women and no one would suggest, based on that alone that they were misogynists. Now if they said women shouldn't be paid as much as a man for a cashier job because men are just stronger than women, then clearly, that's a statement and action of misogyny.