the First Amendment doesn't guarantee that speaking your mind will have no economic consequences. Proclaiming that those without thick skins probably shouldn't marry outside their race is always going to be, let us say, commercially risky if you're aiming for a broad audience — or if your sponsors are. General Motors and Motel 6 both reportedly pulled their sponsorship over the flap, prior to Schlessinger's decision to leave her show. But whether that's the right thing to do or the wrong thing to do, it doesn't implicate the government; it implicates the profit motive.
In fact, the organization of a boycott is itself the exercise of First Amendment rights — GLAAD, or the American Family Association, or Sarah Palin, or Laura Schlessinger, anyone can publicly advocate for an end to the economic support of someone else's speech. If you want, you can boycott them back — "Okay, if GLAAD is boycotting Laura Schlessinger, then I'm boycotting anybody who donates to GLAAD." It becomes reductive and unhelpful at some point, and it may or may not be justified, and one side or the other may be substantively right or wrong — but all of it, from every angle and every political position, is consistent with the idea of free expression.
Because the "free" in that concept means "free from government interference," not "free from consequences."