The thing is the U.S. Constitution's First Amendment, with regards to free speech, protects people in the U.S. from government suppression of expression. It provides little protection from responses, criticisms, or consequences from any and all non-governmental entities.
Probably the most high profile example of this misunderstanding was when 2008 vice presidential candidate Sarah Palin claimed her freedom of speech was infringed upon by the intense critical media coverage. The real tragedy was that Palin failed to realize the First Amendment actually empowers the media with the freedom of the press to provide such coverage of her flawed campaign.
More recently, I heard Carrie Prejean, Miss California USA 2009, who was strongly criticized for her outspoken opinion against same-sex marriage, incorrectly claiming her rights had been trampled on. Interestingly, Sarah Palin released a statement in defense of Prejean in which Palin repeats her mistake in contending Prejean's First Amendment protection was denied.
We must all exercise vigilance when we hear someone claiming their freedom of speech is being infringed upon by anyone other than the government.