There are a lot of parts of American society that are dogmatically ideological but I would say fall short of actual worship.
The biggest dogmatic ideology would probably be American Exceptionalism. That the US is the greatest bastion or freedom/democracy/liberty/capitalism/etc. and is entitled to being the dominant force of global politics. This ideology has been the dominant force guiding American culture since at least the 50s.
When (not if, when,) it comes crashing down it will probably be replaced with some kind of European like existentialism (we'll get to be post-empire Britian then.) Or something else entirely different might happen but it will make the societal trauma of 9/11 look like nothing.
“You have your way. I have my way. As for the right way, the correct way, and the only way, it does not exist.” -Nietzsche
I'd say the state too, people over estimate its powers big style, on both the left and the right, although I'd say on the right wing its the market, they take the whole invisible hand business of out of date economic philosophers pretty literally.