少なくともあなた自身は 見たら抜かずにはいられないほど嫌い、な様ではないようですし
So , what does this な in {な様} mean ?
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Sign up to join this communitySimply, it is な used as part of a na-adjective. Without a comma, do the following sentences make sense to you?
あなたは寿司が嫌いなようだ。 You seem to hate sushi.
試験は簡単なようですね。 Looks like the exam is easy.
If yes, the な in question is exactly the same. Of course, normally, no comma is placed before な, but since this 嫌い is modified by a relatively long adverbial clause (見たら抜かずにはいられないほど), I guess he wanted to make a pause there. You should not do this in formal sentences.