I read about this also. As long as he is a peaceful protester, there is no legitimate cause to detain him. He was exercising one of the rights that encourage people to come here (because often they can't speak out in their countries of origin).

Details are largely unconfirmed, and this might be wrong - but most recent stories report that the government is relying on a provision of the Immigration and Nationality Act that bars aliens whose activities in the U.S. might have a "potentially serious adverse foreign policy consequence" under 8 USC 1182(a)(3)(C):

An alien whose entry or proposed activities in the United States the Secretary of State has reasonable ground to believe would have potentially serious adverse foreign policy consequences for the United States is inadmissible.

uscode.house.gov: 8 USC 1182: Inadmissible aliens

In short, we reserve the right to deny entry or throw out any alien whose presence or activities in the U.S. are causing real foreign policy problems for us. So if the U.S. is trying to achieve some foreign policy goal with the country of, say, Albabia - and there's some alien whose activities are causing a huge headache for the U.S. in those U.S.-Albabian relations - the U.S. can revoke their status and toss them out. This would certainly seem to cover, and indeed be intended to cover, activities that would be protected by the First Amendment when engaged in by a U.S. citizen.

Is it constitutional? Dunno. It's certainly permissible to deny entry to someone who you think is going to engage in First Amendment-protected activities that are going to piss off the Albabian government - that person has no First Amendment rights, since they're not yet in the country. Whether that continues to support a right of ejectment once they're already in the country is a more complicated question....