As a native english speaker, I wouldn't even say "I don't like such music", even though duolingo says that's an acceptable answer. People will still understand what you are trying to say, but it's just not a common thing to say in my opinion. It could be a common thing to say in British english though, what I said refers to American english.
The problem with "this music" is ambiguity. Suppose one enjoys a particular style of music, but simply not the particular composition or rendition referenced by the statement. Though I generally hear the phrase "this [kind/sort] of music", "such music" is also a valid phrase.