I can't speak for all of America, but Bodie's observation is mostly correct in my little corner. Among the young and socially liberal, mental health has as much "stigma" as a Catholic marrying a Protestant. It's not given a second thought. One thing that it can lead to is discomfort and oversensitivity if a normal person finds out about it. That's true with physical illnesses, too.
There are still some Archie Bunkers, though.
Some Americans frown on mental health, just as some frown on interracial marriage or religious conversion.
As long as the mentally ill like guns.