It doesn't matter if the majority believe in it or not, if the 10% control the power (military and police) they can enforce their rules regardless of whether the majority support them or not.
No, even if that 10% included all of the military and police, they could not possibly enforce their will upon the other 90%. It might be a bloody conflict, but they'd lose.
Only if they can convince most of that 90% to comply without overt use of force, is it even vaguely possible to maintain control. If not, they'd be overwhelmed and destroyed in short order.
The only reason it works, is because the overwhelming majority of the population worship the State as a god, and will not deny its power, because that's blasphemous. If they actually looked, they'd see that "the State" is just a bunch of humans in silly costumes, and they'd realize that they are more powerful and don't have to comply with the edicts of those costumed fools.