>your bias
Bias? That I accept, as you do not, that 'contemporary' has a wider definition than "simply allocates a timeframe relationship between 2 or more people or things" to include, inter alia, current/modern/up-to-date.
>clues within the structure allow us to differentiate which might be meant
I agree.
>My version says exactly what the old says, as contemporary is redundant
No. Your version assumes that contemporary is the redundant, understood position for all properties ascribed to the band. And it is redundant for all properties because the band is new. My contention is that you cannot make that assumption. As a result, your version leaves the reader with no idea what sort of a twist the band has put on jive.
I'd accept that it could be redundant in a statement such as
"They are a new, contemporary band"
but even there the particular context may require its use. And yes, you are right, context is of course important.
"A new production of Hamlet in contemporary costume" or "Contemporary critics of Shakespreare" are both ambiguous and either need more context, or to be reworded, in order to make their meaning clear (although you'll no doubt try to argue that contemporary is redundant in the former statement, since it is a new production ...)