I have never thought of American Music as being basically Irish and Scottish..or pan-Celtic. I think it most undoubtedly has huge English roots, as that is the language that was settled on and as you enforce the speaking of English only in schools, only English songs would be sung, in addition to bad translations of Funiculi Funicula. With an occasional French song thrown in.

German songs were probably somewhat suppressed in WWI. Some town in the midwest had tunnels for German-Americans to get about in as they were so discriminated against in that time.

Certainly huge African and Carribean influence.

Some big pockets of Scandinavian music that still exist.

Spanish.

French.

Melungeon influence huge but unrecognized..read up on old-time and Melungeon music. Appalachain music in general. It does not sound Scottish or Scots-Irish (never quite sure what that is) to me. Sounds totally distinct with Arabic influences, and they claim history in Turkey and Portugal.

I actually don't think of this mountain music as The American Music. It is part of the overall picture. Lots of stuff was music hall and parlor music..some Irish, some Hebrew/Yiddish.
Cowboy..I presume Irish, African-American, Spanish all influenced.

Poles and Czechs...most of us did not speak their language..but we still like the polkas and other instrumental music.

But I would side with people who do believe that their is either ignorance about English music or some bias against it. Some of what we sing without thinking too much about is quite insulting to the English and they certainly are not individually responsible for all the woes of the world..they were serfs and conscriptees and coal miners and factory workers and did not have much to say about how their nation was conducting its business...mg