Yes, and it is also broader than just the first amendment. Part of being able to maintain a free society is having cultural norms that do not require employers to fire someone just because they said something that others disagree with or find objectionable.

The first amendment is really of no use if expressing opinions outside the norm causes you to be fired by social convention. In that case, only being independently wealthy affords one any freedom.

In this case, even founding his own organization based on his own values did not protect him from being fired.