There are certain things such as race and gender which are protected classes. It is illegal to discriminate against someone based on these attributes in various ways including employment. [1]
Beyond this, most employment in the US is "at-will", meaning that you can be fired for any reason or no reason. [2]
Some things not explicitly listed as a protected class might still pose problems if its determined that the way in which is it enforced is discriminatory. [3]