According to NY Daily News, Johnny Depp has a problem with actors turning musician. That sounds like a biased slam, seeing as he himself has done just that and finds his own work acceptable.
The truth of the matter is that his line, taken alone as "That whole idea for me is a sickening thing, it's always just made me sick," seems to say just that, but if you can be bothered to hold out until the end of the article, you'll get the real truth of the matter.
Mr Depp continues, "But I hate the idea, 'Come see me play the guitar because you've seen me in 12 movies."
What he's really saying is that he's against the idea of actors encouraging thier groupies on listening to and purchasing their music for no other reason than because of who they are, and not based on the quality of their music or talent.
I myself enjoy Anna Kendrick as an actor, but her rendition of Pitch Perfect's "When I'm Gone" is merely celebrated pish-tosh. In terms of Mr. Depp himself, well, I'd confess to a bit of a boyhood crush, but not to enjoying his music.