As general rule, if you are an "at will" employee you can be fired for any or no reason just like you can quit for any or no reason.
If you have a written employment contract then I would advise that you have a lawyer review it and all the facts to see if you have a claim.
Lately, there have been some state laws propping up that have mitigated how an employer can use social media content of an employee as a basis for termination. From what I understand, they may not be able to request access, for example, to your FB account and would be barred from terminating based on your refusal to give them that access. Your facts, however, are not the same. Here, they simply took issue with your postings and frankly they are not obligated to keep you on if they do not like what you are saying about them. Just because your settings are private is not really relevant as anyone in your network can share that content with them right?
I say this not to be a smart-a**, but biting the hand that feeds you is never a good idea. If you do have complaints about workplace safety your FB community is not the proper forum. There are state and county agencies that you should report those things to and your employer can get into trouble for retaliating against such claims. But rambling on FB is not the same thing of course.
I hope a TX employment lawyer chimes in and offers some insights. If not, I suggest you reach out to one for some sound advice. You can also search for one here by going to the "find a lawyer" tab above.
Most of us here, including myself, offer a free phone consult.
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While I agree with Frank Natoli's answer in most regards, you may have a special case on your hands.
Over the past 6 months, the National Labor Relations Board (NLRB) has been craking down on employers who restrict speach on their employees social media accounts if that speach would be permitted as conversation with fellow employees about the employer and their working conditions (that sentence is a little oversimplified so you could unserstand my answer.)
I strongly suggest you retain a lawyer who specializes in employee rights. You may have a strong case under the NLRB rules.
Andrew M. Jaffe
Attorney at Law
Practice Limited to E-Commerce and Internet Law
This post is provided for general informational purposes only and is not intended to be legal advice specific to you. This general information is not a substitute for the advice of an attorney in your jurisdiction. The attorney client relationship is not established by this post.