The claim that the united states is a post-denomination society is based on a movement:

I believe the answer is: towards spiritualism and away from established denominations

Post-denominations refers to a society that no longer adopt Christian values as the majorities of its principle.

Even if the society no longer adopt the christian values, we could still consider that society as spiritual. But the acknowledgement of higher being in a spiritual society not only tied to the diety that written under Christian holy bile.