Do I have a case in which my freedom of speech has been violated?

I was recently terminated from my employment for a tweet that I posted on Twitter. The tweet did not reference my place of employment, nor was it directed at an employee of the company; however, the person whom I made the comment too, retaliated by filing a complaint with my company, calling me a racist, and I was terminated. My tweet was "Get out of our state and country, Allah lover." It was in response to a Muslim woman who lives in Texas and was making derogatory remarks about Texas, America and our conservatism. HR told me that the reason I was terminated was because I violated the social media policy. When I asked what section of the policy, Jim Kelley, HR Director, became belligerent, raised his voice and said once again that I had violated the social media policy. I strongly believe that this individual has very liberal beliefs and thus his decision was based more on bias than policy. I've never been terminated nor have I received verbal or written warning from any employer.