I only crossplay. Only positive experiences so far. I'm going to share an article I wrote for a cosplay forum because I think the trans community can get something out of it too.
What cosplay taught me about people's perceptions
I' ve been doing cosplay for about 3 years now, mostly Doctor Who cosplay (usually 7th, 10th and 11th) although I' ve also done some Harry Potter characters. I' m 30 years old, female I guess you could say, although I look more like a 14 year old androgynous boy. Short straight brown hair, sideburns, glasses, brown eyes, caucasian, my height is 158 cm and I my weight is average. Now, keeping that in mind, due to cosplay I realized that we only play a very little part in how people perceive us. I think that people's perception of ourselves is based on these four items:
_ A few elements on how you present yourself
_What the other person knows
_What the other person wants to believe
_What the other person is willing to accept
There's also a fifth element of perception, and that is what YOU are willing to accept.
Let me illustrate each item:
_ A few elements on how you present yourself: when we cosplay (and to some degree in everyday life as well, depending on what we want to portray) we try to be as similar to the character as possible (or at least I do). I don't feel comfortable cosplaying characters that never wore glasses at some point because I don't wear contacts. I don't feel comfortable either playing characters with a different hair colour or a totally different hair length because I don't want to wear a wig (Don't get me wrong, I don't care if other people do it, people can cosplay however they want). Anyway, others seem to not even care about the "details" that we put so much thought into, and they are quick to make conclusions. For example, short hair and glasses immediately means to people "Harry Potter". It doesn't matter how your hair looks like, or if your glasses are not round. I can go out in the street with regular clothes and I get people yelling "Harry!" at me. They're not looking at the rest of my features, clothes, etc, they just see short hair and glasses and they associate it. Even worse, last year I bought a 15 cm Tenth Doctor doll (one with glasses), my own mother confused a picture of the doll with a picture of myself because, again, short brown hair and glasses. Nevermind that he is made of plastic and you can visibly see his articulations. Conclusion, people make up their mind based on only one or two things.
_ What the other person knows: taking into consideration what I just said, based on those few elements people also make assumptions based on what they know. For example, I went to a Superwholock convention as the Seventh Doctor. Some people assumed that I was Mycroft because I had an umbrella. They were Sherlock fans who hadn't even heard of the 7th Doctor. I also went to a Comic Con as the Tenth Doctor. I was playing cards with some people when all of a sudden they start yelling "WOOOOO Loookkk!! another Tenth!!!". That "Other Tenth" was a Castiel cosplayer, who gave them the stink eye. She had a good accurate cosplay but these whovians just associated "long coat" with Tenth.
_What the other person wants to believe: part of the magic of cosplay is to make the characters come to life. It's wonderful when it happens. However, to achieve that we may need to overlook certain things. I was at a specialized Doctor Who convention, again as the 7th Doctor and I was playing some board game with people I had just met. One of them said "You even look like Sylvester McCoy". Ehhh...no... what?? yeah, my cosplay was quite good, but I look absolutely NOTHING like him. Thick eyebrows and straight hair, that's it, nothing else, really... nothing. On another occasion I was at a terrible one-room "convention" with an acquaintance. This was a person I had already met before in regular life, sort of president of a Doctor Who fan group. I was Tenth. After a while of being there, bored waiting with her for a caricature to be finished, she looks at me and says "It's weird, but I really feel like I' m with the Tenth Doctor right now". Wow... thank you. Also, at the same Comic Con listed above, while I was eating some popcorn with those whovian people, this teenage girl (a stranger) approaches me and says "Oh my God, I was really hoping to see you!! Can I hug you??". Sure, why not?
_What the other person is willing to accept: at the same convention as well, this 3 year old boy would say "Look mom, Harry Potter! Harry Potter!" every time that he would see me. Eventually, someone in wizard robes turns around, looks at me from head to toe and tells him "Ehhh, are you sure? I think that's a Doctor". I don't think he was convinced.
So how much of people's perception is actually based on how we actually look like? A tiny fraction. Obtuse characteristics like hair length and colour (not even that much hairstyle), glasses or no glasses. In my case at least apparently looks like height, voice, age and/or biological sex, face and body structure does not seem to be an issue for a lot of people. Some could say it's having "the right attitude", but I don't even think I have that, I' m just some sort of Sheldon, cosplay or no cosplay. Every point listed above led me to believe that mostly how people perceive us is outside of our control (I could let my hair grow and probably nobody will call me Harry Potter... although they may call me Ozzy Osbourne then, who knows). Finally, the last point is "what YOU are willing to accept". You can accept what people say or you can think that they are delusional or that they don't know any better, that they are not taking this and that into consideration.
In short, when you cosplay, cosplay whoever you want, people will think whatever they want anyway. In everyday life, just be yourself, again, people will think whatever they want anyway.