Where do people get the idea that the Constitutional 'right to free speech' means you can say whatever you want with no consequences whatsoever? It only means that the government cannot arbitrarily outlaw speech or punish people for saying something they decide they don't like. SOCIAL consequences of free speech are a completely different matter. Should a clerk be able to call a customer offensive names because they have the right to free speech? They can't be charged with a crime for doing it, but they can and should be fired. That is not a violation of Constitutional rights.
But Helen Thomas wasn't even fired! She resigned after many people, exercising the same right to free speech that she did, condemned her comments. No one suggested that she be arrested and imprisoned for what she said. She decided, rightly, that she could no longer do her job properly with this unremovable cloud hanging over her. If she HAD been fired, however, it would still not be a Constitutional issue.
Except for the 'yelling fire in a crowded theatre' situations, speech cannot be outlawed. But that does NOT mean that there should never be any other consequences for speech. We are and well should be held accountable socially for improper things we say, especially when they are at the level of offensiveness of what Helen Thomas said.