At least around people who support you, I think you're obligated to show them the real you. I'd feel better about the all-black comment if I knew that the women were dressing that way for concerts as well, but it does sound like an indication of support. The gender blending approach tends to drive away a lot of people, but there are still others who will embrace it (although finding them can be challenging at times).
A "lobotomy" or something else isn't going to help so much, because whatever treatment you'd hope to escape with is going to change who you are, and the "side effects" are probably going to do more harm than good. I met someone who was studying math who had a eye disorder that caused his eye positioning to shake around, but he didn't want to get it fixed because a typical outcome was diminished ability to study (at least in math). Even if non-conformity was a disorder (and it's not), I still think you'd probably be giving up something valuable to try to "fix" it, and I don't think that the "many" relationships you maybe make afterwards are going to feel as good as the "few" you're making now.
The WPATH Standards of Care say they're "for the Health of Transsexual, Transgender, and Gender Nonconforming People." Even if you identify with your assigned gender, and even if you argue yourself into the idea that you're not transgender as a result (that you only nonconform on expression and not identity), there is still a decent amount of overlap in experience, and you basically belong in the same room. That you've listed your gender as "?" should make you even closer to their situation, because if you do adopt a non-cisgendered identity (trans-binary, third-gender, non-gender, fluctuating gender, whatever), you're unequivocally in their camp, but you need to feel free that you're equally good, your challenges are equally genuine, and your thoughts are equally authentic regardless of the identity you may end up adopting. That we have the androgyne board here (and it fits you well) is a vote from Susan that you're already welcome in this corner of the Internet, regardless of where things go from here.
I think it is misguided for your therapist to give you the idea that you're pushing away people, because that attribution implies you don't want others around you. I don't think you'd be in a choir if you felt that way. Nor do I think you present this way to mess with others. You probably wouldn't be talking about giving yourself a lobotomy if you felt you just had those reasons -- and if you just wanted to mess with people, you'd probably use more variety, do something easier, or take on something that makes you less vulnerable. Your presentation may drive some people away, but that effect is a combination of your presentation, social norms deeming your presentation "weird," and those people taking those social norms to heart, and the moral blame does not lie with you (I'd blame the social norms myself, and the institutions which perpetuate them). If your therapist is blaming you, you probably need a new therapist.
