As for Godzilla, he's a Japanese citizen, so he can't even vote in the US. His overall outlook is certainly conservative, though. Other than that, he's stayed clear of politics his whole "life".
Most of the other actors in G-films are Japanese too. You might see the odd American here or there, but they're usually expats.
One thing though...in 1968's Destroy All Monsters, Godzilla burns the UN building to the ground. Close enough? (I always cheer at that scene)