cringe
Absolutely! I mean, by the time that kind of neckcloth was adopted historically, that kind of lute had been out of fashion for a couple of centuries.
And, have you ever tried playing a lute while dancing without a guitar-style shoulder strap?
And, lute shells are pretty thin - you're really risking damaging it if you're wearing that cut-down-rapier and having the pommel knock against the instrument.
(Also, the dance looks vaguely galliarde-like, which is probably outdated before that style of rapier hilt becomes popular, and was never really taken up as a folk tradition. Or is it supposed to be Irish step dancing?)