I was under the impression that Felix used to "cross-dress", as some put it, as a method to disguise himself. Remember, Felix was a prince, and well-known in his day - similar to the royalty and movie stars of our day. No doubt it would have been advantageous to be able to disguise oneself to get out, and sometimes, as Felix had done, to act out some mischief or be someplace he oughtn't.
If I remember correctly, the first time he did this, he was quite young and did so at the insistence of his brother and a female friend who wanted to take him out to someplace where he wasn't supposed to be. Finding out that they were able to get away with it enabled them to become more brazen over time.
I have a picture of my own grandfather doing something quite similar, and I can assure you, he did not have other effeminate tendencies (well... at least to our knowlege :-)).
Sincere regards,