Yes, almost all folks at Moffett (NASA Ames Research Center) are US government employees, just as at NASA Goddard. They will be on furlough unless their job is essential.

STScI/APL in Baltimore, like JPL in Pasadena, are technically contractors. As described nearby, they are still at work like normal due to the float in money already sent (to Hopkins/APL or Caltech, respectively) but not yet dispersed.

Of course, those folks are looking on anxiously as this fiasco plays out, designing telescopes, probes, and rovers like usual, but with uneasy coffee room conversations.