They probably wouldn't go out of their way to learn a traditional art.
I doubt they'd take the trouble to learn traditional arts.
They might not go out of their way to learn a traditional art.
「彼らはわざわざ伝統芸道を習おうと思わないかもしれない」＝ They probably wouldn't go out of their way to learn a traditional art. / I doubt they'd take the trouble to learn traditional arts. / They might not go out of their way to learn a traditional art.
ボキャブラリー
probably wouldn't, might not ＝ しないかもしれあない
go out of one's way, take the trouble ＝ わざわざ（～をする）
learn ＝ 習う
traditional art ＝ 伝統芸道
I doubt that ＝ （しない）だろうなと思う
イギリス 
