The islander thing has nothing to do with it. Nadal, tennis #1, is from Mallorca too and he is adored. Something about his attitude and demeanor towards others is what rubs people in Spain the wrong way. JL tries too hard to be "chulo" (cool in castellano) and I think comes off a bit as a fake. He would be called a "puto chulo.
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DP on the other hand doesn't even come close to trying. He is seen as much more sincere, and not trying to be something he isn't. He's an introverted, dry and a bit socially inept. Kind of like the nerdy neighborhood kid. He is accepted as that.
MM on the other hand is seen as the happy go lucky, jovial, friendly, playful neighborhood kid that everyone can get along with, or feels they know from the pueblo.
Alonso, on Spanish commentary and interviews can be very much like this too. He doesn't try hard to be cool, and around town he tries to be a normal guy. I sat on a plane up to Asturias once with his previous GF. She was cute, very cute, but didn't draw any unnecessary attention to herself or who was picking her up. On the international scene thought he is very much more serious and business.