The freedom of speech is one of the most frequently cited constitutional rights online. Too frequently, it is cited to justify a person's right to say something that others find offensive or upsetting. However, while most understand that there actually are limits to free speech, just as many are shocked to learn the freedom of speech doesn't actually apply to any of the websites they are likely using.
For starters, the First Amendment only protects people from the government restricting their speech unreasonably. For instance, it does not protect people in real life, or on the internet, who incite violence; nor does it protect people making credible threats of violence.
Since websites are privately owned, websites are free to develop their own policies regarding what is or isn't allowed. You will generally have no legal recourse if a website chooses to censor you (although if it is done discriminatorily or in violation of a contract, you may).