The employer is allowed to request only "natural" looking hair colors. They want you to look professional and approachable, not immature (I know it's a generalization, but some people do indeed find people with funky hair unapproachable, immature, etc.).
BUT there are plenty of places that will hire you even if you do have "unnaturally colored hair". You just have to look around. Remember though, having an income is MUCH more important than having purple hair, so learn to prioritize and don't be unwilling to make a sacrifice in order to get a job. Dying your hair a different color that's deemed acceptable by your employer would not be a big or life-ending sacrifice, trust me.
Also, not EVERY teenager dyes their hair weird colors or in general. I never did when I was a teen. I still don't now because well, I like my natural hair color.