The New York Times on Sunday ran a front page story “Visa Screening Missed an Atacker’s Zealotry on Social Media”, by Matt Apuzzo, Michael S. Schmidt, and Julio Preston. The details of the story are about Tashfeen Malik, whose apparent support of violent jihad was event in social media to anyone who looked. Homeland Security had apparently not started looking even at public social media until recently, and had not determined what screening was appropriate, even for public postings.
In fact, apparently DHS forbade agents from looking at social media of applicants, fearing bad public relations (ABC News). But Fox, NBC and CNN report that Malik's page had been private and in the name of her sister.
Of course, a lot has been reported over the years about employer probing social media, especially during the hiring process.
The First Amendment would preclude government’s taking action against someone already in the country for lawful speech, but not for making threats. The analogy is to the Cold War days with speech advocating “overthrow of the government” or violent “revolution” would have been illegal (and the country got carried away with this, as in the movie “Trumbo”, on Movies blog, Nov. 13.)
As I've related before, I had an incident involving this issue in 2005 when work as a substitute teacher (as a public employee with First Amendment protections).
But exclusion based on speech could be more easily applied lawfully against someone (a non-citizen) not in the country.
Applying the situation in reverse, people with controversial social media content might have a much harder time in the future visiting authoritarian countries like Russia.
Update: Dec. 14
The the Washington Post editorial "Social media sites don't need government to shut down terrorists", Diane Feinstein (D-CA) has a bill to make monitoring mandatory. I expected Electronic Frontier Foundation to post a piece critical of her bill today.