Sauron was just a representative of Melkor in the Second and the Third Age, and I think that was enough of a reason for the elves to hate him. Each of Galadriel's brothers was killed by Melkor's minions (Finrod by Sauron), as were also her uncles and most of her cousins. And think what happened to Celebrķan.
If we're talking about personal vendettas here, Galadriel would have had much more reasons for that than Elrond.
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He bit me, and I was not gentle.
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