So much for freedom of speech in the west, eh?
Do not confuse "freedom of speech" with meaning that there are no repercussions for speaking out. It mainly means that the government cannot prosecute you for speaking your mind.
Say someone runs a store and insults my mother. I have the right to stop shopping at that store. I am in no way infringing on his freedom of speech. He has every legal right to say what he said and the government can do nothing about it. That does not mean that the people who like my mother cannot decide to take action by boycotting his store.
Helen Thomas has every legal right to say what she said. She broke no laws. She will not be arrested.
If the company she works for wants her to leave, though, that is their right also.
Now if the government had decided to arrest her or fine her for saying what she said then you would hear an uproar over freedom of speech.