While I don't think that she is a "racist" largely because that is a condition of the heart, and I don't know her, or her heart, I do believe that what she said is at the least inappropriate, and her company is within their right to let her go.
BTW, The constitution largely is a document stating what the government can not do to you the people. It has little to do with private companies and their reasons for firing an employee. She has the right to say it, she also must accept that it was a dumb thing to post on social media.
Americans are so enamored of equality that they would rather be equal in slavery than unequal in freedom.
Alexis de Tocqueville