You're performing two different versions of E.H. Brogan and those versions don't get along. The "Icky Feeling" is the cognitive dissonance caused by their failed reconciliation.
On the one hand, you have chosen to define yourself by the things that you have done to your body. This gives you ownership over the meat you inhabit because you have done things to it that distinguish it from every other bag of meat out there. On the other hand, you practice a profession in which meat is unimportant and the emphasis of meat is viewed as unprofessional. You have enough enthusiasm for this profession that you are willing to subvert your meat celebration but you resent it. You also recognize the threat your meat poses to your profession, and your profession to your meat.
All the piercings and hair dye and tattoos and Manic Panic in the world do not define conservatism or radicalism. They are only the banners and flags. Ideology is mental, is internal. Your employer class does not wish to be reminded of your meat modifications because they provoke a conversation - that is their fundamental purpose - that is off-topic to your profession. Everyone else at the office has either chosen to cement their cultural allegiances in ways that do not distract the customer or has accepted that we are not what we wear.
You need to wave your freak flag. That's fine. Your employer doesn't want any flag-waving. That's fine, too. But the core issue is not your employer's resentment of your freak-flag - it's your need to define yourself by your performance.
Maybe this is why I try to post publicly whenever possible: I am proud of my life. I am proud of what’s in my head. Proud of who I am. I know not everyone will like me, these things that I have grown to become a me I want to be. But I do not want or need anyone who would want to know me because of how I look in photographs. I want those who read what I write, and like me anyway - maybe even, in a dream, like me more because of it.
And well you should be. What you need to understand is that employers care not a whit about your individual peculiarities. They care about your chosen expression of them. Regardless of how conservative and straitjacketed you may think an organization is, I can guarantee that there dwell within it people whose background is tawdrier than yours, whose hardships dwarf your own, whose perversions would make you blush and whose passions are even further from their workplace. You won't know unless you ask, though. They have found ways to be that don't violate a dress code.
Youth is a period of external reinforcement of identity. That reinforcement becomes internal with time... or stands as a hallmark of arrested development. I still have hair longer than my wife, in quintessential Espanola Valley Skatefag trim, and I'm a 40-year-old man. No tattoos, though. My identity performance has tempered itself to the point where I blend almost everywhere.
My passions are no dimmer.
There will come a time when you will know it without saying it, you will show it without wearing it, you will be it without performing it. And then the dichotomy will bother you no more.