Lox: In folk music, we need to distinguish the strictly modal (in the medieval sense, and that requires just intonation to really fit the bill) from modern "modal" usage. As I said earlier, modern "modal" music is not restricted to just the natural scale tones; "mode" relates to the predominant scale and intervalic relationships relative to the tonic. But modal music can vary just as flexibly as major/minor music can. Major tunes can have II chords that really function as VofV (a temporary change of tonal base, but not mode) or can incorporate accidentals in either melody or harmony, and yet they are still considered "major" because the overall patterns fit our expectations of major tunes--including most of the divergences from the natural scale. So also with tunes in other modes. In fact, the different ways that the diminished triad (occurring in more prominent harmonic position) is used, avoided or modified in the various modes is part of their characteristic sound.

An example is Lydian, where the diminished triad is rooted on an augmented fourth. A common method of avoidance is for the harmony to shift between I and II, or I and V. However, you're also likely to hear the IV root lowered to the perfect fourth, while the melody may continue to use augmented fourths! The somewhat discordant result (and the prominent tritone generally) is one reason I particularly enjoy Lydian mode, and have composed several tunes in it.

dr.tom: For similar reasons, authentic and plagal modes don't generally apply when discussing modal folk music, because folk tunes aren't artificially limited in range (except, perhaps on instruments like pipes.)