Cf. def'n 2 http://www.larousse.fr/dictionnaires/francais-anglais/type/79391 Checking Google NGrams "type de musique" and "genre de musique" are close to tied as of 2008. Incidentally, "type d'art" is actually about twice as common as "genre d'art."
I can imagine uses for "Don't listen to that type." As to whether this particular French sentence could plausibly be interpreted that way, I defer to others.