I kind of go both ways on this. He obviously has a right to speak his mind, and we can't infringe on that. You want to take extreme positions, publicly, I have no problem with that. But I don't have to employ you either.
I own my own business. I have employees. If they choose to walk around with a t-shirt that says "F *** Y**" on it all day, it's their right. But I don't know that I'm going to continue to employ them.
As a business person, you have to walk a fine line. If you choose to be too extreme with limiting your employee's behavior, you end up constantly turning over your workforce, and that's bad business. That's why you see employers choosing to generally ignore things like tattoos, piercings, etc..., that if I had worn 35+ years ago when still actively seeking employment I would have been kicked out the door.
My guess is this professor gets reinstated. Public employees usually end up with special protection regarding free speech rights in the workplace. But in the real world an employee has a choice to make. You can exercise your right to look like an a $$, but you run the risk that everyone will suddenly discover you are an a $$, and that can sometimes make it hard to hold a job.