Most government-run museums definitely allow cameras (heck, you're allowed to paint at the national art gallery, they even have easels for people so I don't know why a camera would be a problem there). A lot of Asian tourists have what we'd consider "professional" grade camcorders in the US and I've seen a lot of them in the museums here. (Not sure if I've seen any people with tripods).
The only places I can think of where they definitely won't let you use a camera is the mint (they don't want people to record how money is made) and the spy museum (which is privately owned).
If for some reason you do get turned away from a museum, try another entrance or wait for that particular guard to get off his shift. Someone else might be more lenient. Good luck!