I am not licensed to practice law in Texas so the following should not be taken as legal advice, but simply as information based on general principles of law which is intended to educate. If you need legal advice, please consult a lawyer who holds Texas licensure.
At will employment means you can be fired for any reason, including a foolish one, except as to those reasons the law says are impermissible (gender, race, national origin, religion, color, age, etc.). There are a few other reasons that the law says just aren't allowed, such as retaliation for filing a worker's comp claim, reporting crime to the police, or cooperating with a sexual harassment investigation. But apart from those rare exceptions, that's it. If you are an at will employee and your boss doesn't like you, he can fire you. He can fire you because you chew Dentyne and he doesn't like gum chewers. He can fire you because he doesn't like your haircut or the color of your socks.
An at will employee can be fired because the employer does not like the employee's shoe laces.
Only if a protected class discriminatory reason is one used to fire an at will employee would be one that may give some protection.
You might read my Legal Guide "What is a Civil Right?"
Good luck to you.
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Sorry, you don't have any rights because you are working without a formal written contract. Anti-discrimination laws do not guaranty civility in the workplace.