I think the best approach is to try to learn to play both ways - for different effects on different occasions. I double-stop strings on the fiddle and mandolin, but sometimes you may need a more separated sound, and then it may be better to move the finger over. Likewise on the guitar: A lot of my own songs would be impossible without using the thumb, specially those in non-standard tuning (which the classical people never envisaged), but being able to shift into classical stance with the thumb in the 'correct' place is useful when working up the neck. Actually this applies to wrist position on the fiddle too. Flat hand is handy for fast tunes, but if you can also arch back into the classical position you can introduce vibrato if that seems approppriate on, say, a song.