Maybe a member plays an instrument you can’t stand, or the singer’s voice irritates you…
Not sure if this is what you are asking, but I like Black Sabbath’s “War Pigs” just fine, but I love Faith No More’s version of it much better.
Aye, there’s plenty of covers that I like better than the original, but that doesn’t seem to be what the OP is asking about. Generally, if I don’t like listening to a band, I don’t go seeking out their material in other iterations.
The Beatles have a few good tunes, but I can’t stand their vocals. Blackbird covered by Crosby, Stills and Nash comes to mind.
Something like this?: not being from New Jersey, I never “got” Bruce Springstein. Nothing really against him though, just not my milieu. But I do like covers of his songs and people inspired by him.
I suppose some Bob Dylan applies as well.
I’ll have to ponder this one for a bit.
I usually seek out covers of bands and their songs I like in order to hear the reinterpretations. I sometimes enjoy when bands I like cover songs of bands I don’t much care for. But I cannot think of any bands off the top of my head whose covers I actively seek out when I don’t like the original band’s sound.
moi aussi
one of many of my examples for that would would be:
not sure if this is quite the inverse of what the OP is asking but, The Band’s “The Night They Drove Ole Dixie Down” is the only version - covers are unnecessary.
Bob Dylan
Tim Buckley
The Doors
and possibly Kraftwerk, I might be on the fence about that one - my favourite Kraftwerk songs are the covers of Hall of Mirrors by S&TB and The Model by Big Black, but I like Kraftwerk well enough…
Bob Dylan writes great songs for others to turn into great covers 
I love nearly all covers of David Bowie’s songs far more than the originals. Bowie was a fine human being, but I just never “got” his style, for some reason.
I second/third Bob Dylan.
I don’t but my wife can’t stand listening to Leonard Cohen sing (although she appreciates him as a writer). So she’ll enjoy most covers of a Cohen song but not the originals.
I generally hate the synth sounds and production of Depeche Mode originals, but I generally like covers of them.
e.g. Nouvelle Vague - I Just Can’t Get Enough