It does sort of baffle me that your parents would be getting worried over what sounds more like a faux-hawk or shaved back/sides kind of cut, which is not all that weird or uncommon and is pretty easy to cover, pull back, or style if unsuited to a job or formal event. If their concern is whether you can get a job, I would suggest framing it like that. If it's that people will judge you negatively, remind them of your good behavior, etc. If they still won't allow it, there's really no option but to get rid of it.
Personally, when I was your age, I didn't ask for permission to dye my hair, I just did it. I knew that I would get funny looks and didn't really care (partly because my clothing drew funny looks anyway). I also knew that I could easily cover it at my job. I did get yelled at for dying my hair before high school graduation, but in retrospect it was a big public event and I gave no warning. Generally, though, my parents' attitude was that as long as I maintained good grades and stayed out of trouble, I could do what I liked with my body (as long as it was legal, obviously).
You're a guy, I don't see what the big deal is. In high school, a lot of the guys would shave their heads into mohawks when they won a big game (I couldn't tell you why though lol). It's not like it's purely associated with this punk-ass druggy culture, especially if you don't dress like an obnoxious emo/scene/whatever the hell kid. However, if your hair is any longer than a centimeter and you're not spiking it, I think it usually looks worse than just a straight-up shaved head, but that's my opinion. I'm also making huge assumptions since I have absolutely no idea what you look like
I've been weary of trying to spike it. I think I should try it Crazy guys you have at your high school LOL
I was kind of inspired by Chris #2 of Anti-Flag. He used to have a fauxhawk kind of cut that wasn't spiked upwards. [link] There are cool images here of deathhawks. [link][link] My hair is still in the experimental stages, so I'll be trying to find variations that I can do.
So... they think shaving your head (the result of cutting off a mohawk) is preferable to a mohawk? A hairstyle that's been seen in youth for at least 40 years? There's even such a THING as a "liberal" haircut?
A real mohawk consists of hair left growing in the center of the scalp only in a strip running from front to back, the rest being shaved clean. If you cut a mohawk off, you're left with a wholly shaved head.
If you instead have some kind of faux-hawk, sounds to me like they're making a whole lot of noise over very little.