No it isn’t. That is the very distinction that free speech advocates need to make. Your political speech as a private citizen, made out of uniform, and not on company time, should not be subject to regulation by your employer. However once you sign a contract and put on the uniform, your speech can be constrained while on company time. The employer can legitimately say I don’t want my workers antagonizing paying customers and fans when those workers are on the clock. You can order a Big Mac and know you will not be politically harangued by a high school kid in a MAGA hat.
Another case similar to Robertson’s was Kurt Schilling’s: fired by ESPN for social media posts made on his own account on his own time. I agree corporate censorship is a real danger, but I don’t think there is anything disingenuous in making a distinction between what is done while an employee on the job and what is done as a private citizen.