People who describe a broad swathe of American music as 'Country and Western' are merely showing their ignorance of a rich and diverse musical lineage. Would they describe Jean Ritchie as 'C&W'? What about the huge repertoire of fiddle tunes played in bluegrass? The vast number of historical ballads in the old-time repertoire? The social commentary of songwriters like John Prine, Townes van Zandt, Guy Clarke, Loudon Wainwright and others? Where do Phil Ochs, Tom Paxton, Bob Dylan and company fit in? Don't get me started on the origins of country blues and Texas swing...
I agree that an entire evening of American music in an ostensibly English folk club would be a little incongruous, but the level of intermingling between traditions means that hardly anything is impossible to justify as appropriate. A small example; I was playing mandolin in an 'Americana' session recently, and as part of a set of Old-Time tunes swung into 'Harvest Home', usually thought of as an Irish hornpipe, but often heard in Morris. I was glared at, and later told that 'we don't really appreciate that diddly diddly stuff here'. I replied that the tune I played has another name in the old timey tradition; it's known as the Cincinnati Hornpipe.
There's really only two sorts of music, in my view; good and bad, and I'm ok with bad as long as you play it like you mean it.