There are cases and cases:

1) Music that is anachronistic because the writer/director/producer/musicmaster got it wrong. There are probably many cases of this that are unknown to this day because nobody knows.

2) Music that is anachronistic on purpose. Case in point is the brief but intense series "The Knick" which takes place in turn of the (last) century New York City, but has very modernistic music.

3) Music that is anageographic(?) The famous use of bazouki music in "The Third Man".

4) The case of it's just music. I'd put forward the memorable "Dueling Banjos" and the use of "Ashokan Farewell" in the Burns Brothers Documentary "The Civil War".

And Butch and Sundance will always have "Raindrops".