Not sure who's dumber -- the person working for the City that decides this is actually a good idea, or the person applying for the job who actually gives them their user name and password on the job application.
This reminds me of the Milgram Experiment, in that very few will refuse authorities orders on even severe matters (in the experiment it was potentially killing someone), so why are people going to refuse it on something seen to be as trivial as a facebook password. However, this is a breach of one of the fundamental human rights, the privacy of thought which in the US has been extended, in some cases, to entire laptops at border crossings.