I saw an interview with either the director or writer where they commented on Fozzie being stupid. But outside of the 1990s, Fozzie usually isn't stupid, or at least not that stupid. I'd say he's at least a little smarter here than in MCT, MTI, and MFS. Though it seems the Muppets in general are kind of portrayed as stupid here. Or maybe just a bit too naiive (though they have been naiive in other productions as well).TMM had his whole introduction scene, GMC he was playing an investigative reporter, MTM he had that part at the end of the film backstage with the polar bear joke, MCC he had his one scene of comedy, MTI and MFS changed his character to a mentally challanged comedy relief, and TM'11 had that scene where he is doing a comedy act, yet not once in MMW does he have anything to do with comedy, and there is no excuse like he is playing a different character or that the writer does not know Fozzie's character,
Back on the subject of whether the others know Kermit and Constantine look similar and such, at the wedding scene, everybody is surprised that there are two Kermit's, but once Constantine rubs the make-up off from over his mole, everyone is in shock, like they know he's Constantine and were not expecting this other Kermit to be him.