Fine dining appearance requirements

I’ve been serving for about 3 years now and have been in the restaurant industry for about 7. I love my serving job (it’s pricey but it’s outdoor and the vibes are super casual, almost to a sports bar level) and make great money but the hours aren’t always consistent. I was considering getting a second serving job but the money at my current place is so good that I really wouldn’t want to go anywhere where I’m not making comparable money. I average $35-45 an hour, and i feel like the only place where I can make comparable money is fine dining. However, I like to have some streaks of color in my hair and though I get it professionally done and maintain it well , I’m usually told by friends that I would get turned away at pretty much every fine dining restaurant because of my hair. Does anyone have experience with this? Is it really that strict?