We live in a free country, and freedom of speech is a fundamental right. Part of our freedom is the right to seek gainful employment wherever we choose and the right of employers to set (reasonable) terms for such employment.
An NFL team is an employer, just as is Delta Air Lines or any other company. As such, it has the right to set terms for conduct in the workplace. Imagine how an airline might react if their pilots or flight attendants chose to wear protest garb vs. company uniforms. Sorry, no can do. Similarly, an NFL team has the right to tell players what they can and cannot do while on the field, while engaging in the workplace for which they are being paid.