You're obviously better positioned than I am to know but I think it's about a popular image rather than how opposing fans might feel about him. There are massively successful sports stars who remain popular despite the fact they can destroy opposing teams' supporters' hearts: say Messi. Even Real Madrid fans struggle not to like him, whereas Ronaldo divides even Real fans, despite being almost as good as Messi, and has generally become something of a pantomime villain within the game. You'd know better than I do if that's the case with LeBron but I definitely think some players have a 'likability'/'dislikability' factor that goes beyond success and team rivalry.
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