Is it legal for my boss to tell me to not speak Spanish at all at work even with my Hispanic co-workers?

Freedom of speech only applies ot government activity (e.g. by a government entity, like an agency, the courts, public schools, etc.), not to private businesses: private businesses do *not* need to allow freedom of speech, and the first amendment does not apply to them.

Whether there is any possible cause of action depends on the context and your location. Some states, such as, I believe NY and CA, prohibit discrimination and harassment at work based on national origin; many states, however, do not. If you are in a state that prohibits national origin-based discrimination, *and* telling you to not speak Spanish at work could be seen as harassment of you based on your national origin, you may have a legal action. However, be advised that it's been found to be the opposite in some cases: there are cases in which allowing workers to speak a language other than English at work is taken to be harassment or discrimiantion against English-only speakers in the workplace. It is therefore far from a given that even if you are in a state that bars national origin-based discrimination, that waht your employer is doing would be improper. (There are also business reasons to bar other languages in the workplace: to facilitate communication with English speakers, avoid factionalizing the workplace, etc.)

While you can consult with an employment attorney to reivew the situation in more detail, there is a good chance that your employer may ban Spanish in the workplace.