This is really the strongest argument I've seen of any of this being a problem. Coming to any country as an immigrant is a privilege, and it the immigrants prerogative whether or not they feel the terms are acceptable. It is, however, completely unacceptable to put a special burden on their citizenship like this. Once they're a citizen, they should be a citizen, period. If there's not confidence that they're acceptable, they shouldn't become a citizen in the first place, otherwise they should be treated with full rights.
I'm not clear on how dual-citizenship works when you naturalize to the US, but are there not situations where they have to give up citizenship to their country of origin? Does that mean these people are permanently left in a degraded legal state with no home country, where they would have full legal rights, to return to should the DHS decide they've over stepped their bounds on Facebook?