Haruo said:
As for American fasola, the groups I've heard don't change the names of the accidentals, and not uncommonly treat them as nonexistent in practice (i.e. when singing the tune in fasola, tend to sing the natural when the music calls for a sharp or flat).

Actually the way I've been taught it in Sacred Harp is that the sound/name of the shape note is changed slightly when you sing it, i.e. sol becomes see, fa becomes fee, etc.