Important phrase to remember: "employee at will."
Outside of a few professions (e.g., ahem, tenured professors, certain negotiated union contracts), most people in USA are one. And it means the employer really doesn't need a reason to terminate.
You're protected more if the discrimination is based on a particular class of criteria (e.g., race, gender, sometimes age, religion, sometimes whistleblowers), but those classes are very few.
And dress alone is not one of them.
A lawsuit would likely be a PR disaster for the employer here. But my guess is that he'd win pretty easily.
And do not be conformed to this world, but be transformed by the renewing of your mind, that you may prove what is that good and acceptable and perfect will of God.
Romans 12:2 (NKJV)