Mr.Cox must see himself as pretending to be a woman
Why wasn't he insulted by even being considered for this role. He should have been outraged. His response should have been, "why me? Did you ask Lady Ga Ga or Lea Michelle?" He didn't react that because he knows why they weren't considered, because their not pretending to be women, they are women. In his heart he knows he was asked because he's pretending to be a women, just a bit more committed than the original Frankenfurter.
I would have a lot more respect for him wanting to seen and referr d to as a women, until this choice, because this shows me that she knows he, even if it is unconsciously, knows HE is pretending