Are hair salons allowed to mandate a dress code?

I’m a hair stylist and applied for this job at a very posh salon. I would love to work there but the policy is all black, head to toe. Women must wear long sleeve black sweaters and leather pants (vegan leather exception for vegans) and men have to wear black fitted t-shirt and black slacks. Shoes/boots must be black.

is this allowed?
Are hair salons allowed to mandate a dress code?
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