Hi Ashley,
It's never easy being discovered, even worse when you can't control how other people find out. I learnt that the hard way and lost a whole bunch of friends which caused me to retreat further into my shell, purge and even contemplate ending everything so I really do feel for you. Over time I accepted it wasn't my fault, it was simply just the failings of some people being very close-minded. I've read a few arguments that state you should respect your father in laws rules but I don't see an example of his so-called manual of what is approved and what is not approved. Is it posted somewhere for you to see, perhaps on the fridge door? Personally I don't think it's your fault since he clearly can't wrap his head around the reality of the situation and quite of few of us will know that we can't always control our need to dress up. Your wife clearly doesn't have a problem with it and supports you.
I think there would be a more valid argument for your FIL if you'd been doing something inappropriate (unless someone is trying to say gender expression is inappropriate) but you weren't and you're right it changes nothing about you as a person but some folks sadly don't see that, they just make stupid assumptions and start to play the moral judgement card as an excuse for their lack of understanding. You could certainly try a letter or a face to face talk but I get the feeling from some of the things you've said it might be pointless. I personally would just move out because I don't like being around bigots but it's harder for you because you have to consider whether your wife is okay with being distanced from her father. I hope you work something out, but having to stop being who you identify as just to suit someone else's delicate sensibilities totally stinks and don't for one minute let him touch your clothes and throw them in the garbage, you have rights hon and that's your stuff. Stay strong!
Crystal x