I always get confused by that one, so I actually went and looked it up in my Webster's Dictionary of English Usage. It claims outright that nonrestrictive clauses must be introduced by ``which'', and that restrictive clauses can be introduced by either ``which'' or ``that'', depending solely on stylistic concerns. So, by that rule, I don't think I could be wrong. In reality, I'm not sure whether ``that are albums'' modifies ``playlists'' in a restrictive or non-restrictive manner. I'm leaning towards restrictive, though, so you might be correct also.
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Bitt Faulk