"Free speech" as a right means that the U.S. Government or State Government can not knock on your door at 3:00 A.M. and haul you away to prison for expressing a political opinion.
"Free speech" does not protect you in any way from being chewed out by your boss, called an idiot by your next door neighbor, berated by your clients or, in the case of performers such as the Dixie Chicks, boycotted by your fans.
This particular reviewer was so closely associated with City Hall that his views would reflect directly on City Hall.
Certain jobs require a certain degree restraint because of the public image they project. If, for example, you work for U.P.S. and your boss sees you on the Channel 5 Nightly News wearing your UPS uniform at a demonstration carrying a sign that says "No Blood for Oil" or "Pro-Choice is Pro-Death" you would have put UPS right in the middle of a fight it wants no part of. The next day your boss would be giving you either a severe tongue-lashing or giving you your pink slip.