I find it useful to go back to the source from time to time, just to remind myself what we're actually talking about.
Here's the First Amendment to the U.S. Constitution:
our founding fathers said:
First Amendment
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
There are actually several separate bits to the amendment, jumbled together. A bit about religion, a bit about the press, a bit about assembly, a bit about petitioning the government for redress. In short, parts of the amendment have nothing to do with this instance. So I highlighted the bit that does, so that we can isolate and focus on it:
Congress shall make no law abridging the freedom of speech.
That's it. That's how the 1st Amendment applies to the case of an idiot posting reprehensible things online in response to a thug hitting a co-ed.
Since Congress* clearly didn't make any law abridging this idiot's ability to speak out, we're done. Can put the First Amendment to the side, we passed that test. It has no further bearing on the issue.
Because what the First Amendment does NOT say is:
-- You can applaud or encourage violence without consequence;
-- You can keep your job even if your employer finds out you are a cretin;
-- The First Amendment is only about political speech;
-- You can insult others and use socially charged phrases without people judging you and responding in ways you don't like;
-- The internet is a consequence-free zone.
Some folks in this thread seem to think one or more of those things are true. None of them are.
So that's the First Amendment sorted.
Go Vols!
* The First Amendment actually applies beyond Congress to state and local government, as well. There's a somewhat complicated history behind that involving the 14th Amendment and a whole lot of Supreme Court cases back in time.