It's actually E dorian/minor hexatonic with a"pien" sixth (the C sharp that makes it dorian can be omitted without changing the tune in an essential way).

Tunes that aren't major or minor are pretty common. I presume you got that from Sharp & Karpeles, 80 English Folk Songs from the Southern Appalachians. Looking through that book:

1 minor/dorian/mixolydian pentatonic
2 mixture of mixolydian and major
3 dorian
4 dorian
5 major
6 lydian/major/mixolydian pentatonic
7 mixolydian
8 dorian/minor/phrygian pentatonic
9 lydian/major/mixolydian pentatonic
10 major/mixolydian/dorian pentatonic (this is very unusual)
11 mixolydian
12 lydian/major/mixolydian pentatonic
13 mixolydian with a major final cadence
14 ditto
15 dorian
16 dorian/minor hexatonic
17 dorian/minor/phrygian pentatonic
18 dorian/minor/phrygian pentatonic with pien 2nd and narrow range
19 dorian/minor/phrygian pentatonic, plagal
20 mixolydian with a 6th gap, narrow range

And so on. I think modal variety was one of their selection criteria.