Earlier quoted context omitted.
Not in California. Political activity off the clock is legally protected. Because it isn't ever actually carrying a swastika flag. It's supporting the opposite side of a current contentious issue like abortion.
Making a hostile environment at work probably isn't protected, though, and that's what carrying a swastika flag on national television will make. As soon as I know a coworker is running about carrying a swastika flag, I can never feel safe around that coworker again.
Treating everything about a person as within scope for personal concern is one of the things that really strongly turns people against each other. It shouldn't matter what someone believes or does on their own time, whether it's a right-leaning company with a gay employee, or a left-leaning company with a right-leaning employee.