Meantone tuning is the norm in historically clued-up performances of Renaissance and Baroque music - there were many variants of the idea, but they all tried to get thirds better in tune. (In mediaeval music, thirds were thought of as dissonant, so messing about with the tuning to make them sound better was irrelevant; fourths and fifths were what mattered).

Scottish traditional music is in some ways a dialect of Baroque music. Connections with Middle Eastern music are a bit of a fluke, but learning to listen microtonally helps with both.

As Sean says, singers tend to like more harmonious temperaments when they get the opportunity. To me a piano in modern tuning always grates as a vocal accompaniment.

Aren't anglo concertinas often tuned in meantone? If you're only playing in two keys there's no need for equal temperament.