I think it's useful to know about modes but for the purpose of harmonization. There are modal cadences in chord progressions that define the character of a melody. Sometimes it can get confusing since there is a version of Greensleeves that is Aeolian and one that is Dorian. Changing the one note makes a difference. On the whistle,
E,G,A,B,C#,B (Dorian) E,G,A,B,C(natural),B (Aeolian). The selection of chords you use would make the difference and define the mode. The problem is that it can be played with a D# later on in the tune which would knock it out of the Dorian mode (as against a V chord). If it's played with a D natural against a V minor chord, it's pure Dorian or Aeolian.

On Drunken Sailor, the progression i minor to bVII major is used in both Dorian and Aeolian but the bVII becomes less important in a tune that emphasizes the Dorian scale. That sneaky little C# makes it a Dorian tune even though the chord progressions spell out more of an Aeolian flavor.

The question is why bother with modes? Why not just play the notes? In folk music, certain tunes retain an individual character that are modal and to recognize these is a useful musical tool. It helps when you go to harmonize the tune. I think the harmonic implications of the tune are just as important as the tune itself. To emphasize this point it would be helpful for guitar players to play:

E min to A major (and secondarilly D major or b minor) to hear a Dorian cadence. (i minor, IV major and bVII major or v minor)

E min to D major (or b minor) to hear and Aeolian cadence. (i minor to bVII or v minor)

E major to D major (or b minor) to hear a Myxolydian cadence.
(I major to bVII or v minor)

These cadences are implied in Irish music in tunes and songs and are the principle modes for this kind of music with the exception of the major scale or Ionian mode which is the standard E,A,B7 or I,!V,V progression.

This doesn't mean that you would have to exclusively stick to the modal harmonies. You can reharmonize to jazz it up if you like.
For example, you could use Emin, G major and F major7 to emphasize an Aeolian cadence. Many Irish tunes are harmonized this way.

Frank Hamilton