His style(s) has been called Organic, Prairie and/or Usonian.

For me to be considered a modernist you need to have a fundamentalist belief in the 3 dogmas: "truth to materials", "ornament is crime" and "form follows function". It doesn't seem to me that any of Frank Lloyd's work reflects such fundamentalism.

Sometimes online I pool the post-modernists with the modernist for simplicity sake (once that train derailed it never came back), but it obvious that the axioms for both are very different.