The public certainly has the right to boycott an artist's work if they committed a morally reprehensible action without any sign of remorse. The public doesn't owe the artist anything.
Calling Yusuf "Cat Stevens" Islam "disagreeable" is a euphemism, he is a bigot and an religious extremist of the worse kind. He wants people to get killed for their ideas although I bet he didn't even read Rushdie.
It has the right, it's just stupid to exercise it.
It's not as if we should only consume art made by good people. Or that whatever bad things an artists does in their personal life has much bearing to wether their art is any good (not to mention most good and bad things in one's life improve art: they instill it with life experience. Boy scouts seldom produce interesting work.).
If you want to punish the artist for something they did, put them in jail. Or don't be friends with them.
If they produce good art, and you don't listen to it because they are bad, you lose too.
>The public doesn't owe the artist anything
Well, if they listen to his works, then they owe him on that.