Welcome to the United States. Federally speaking at least, there are very few protections for hiring/firing. You can be fired for your hair color, unless the hiring manager is as much of an idiot as he is an asshole and says "black people don't have blonde hair" (happened in a Hooters case I remember reading). The company policy reads "right hair color for your skin tone", and is actually normally enforceable in the US because it's implying no "unnaturally dyed hair". They hypothetically can turn away an Asian redhead with no legal ramifications so long as she dyed her hair that way.
So yeah, they can 100% not hire you because you're a Scorpio. More realistically, you'd probably see someone who doesn't hire Aries, Virgo, or Aquarius because the New York Post had an article claiming those three signs are more likely to get fired.