The employer can fire you if you don't have any right to continued employment. Unless you have a contract for your employment, you are an "at will" employee. At will employment can be terminated at any time by either party, for any reason not prohibited by law. As to the employer, it can't terminate you because of a reason that triggers unlawful discrimination (age, race, sex, religion, national origin, disability, etc), retaliation for exercising legal rights, and that's about it. The employer can terminate you for wearing blue, or because Farve is a Viking, or because of that Balloon Boy fiasco.
A very few states have protections for your completely personal life. Check your state's department of labor website.