Get used to it. As a Yankee fan, I hear it all the time regarding Jeter and Arod. Let them hate. Most of the time, the hate is hilarious and you just have to sit back and enjoy it. You get some legitimate laughs sometimes (come on, some of the Twitter stuff that got posted overnight was hilarious).
It doesn't bother you after a while, I love it when MLB-age shits on Jeter being "shitty" or Alex dating some has been wrestling chick, because they have that chip. It'll bug you less when/if you get that chip.
I think a lot of it still has to do with the way Wade/Lebron/Bosh came together and how much pomp and circumstance there was. Then they announced they'd win multiple chips ("not one, not two..") and put expectations on themselves. It's similar to how the Jets are crashing and burning right now.
It's good that the Lebron hate amuses you, it's gonna be there until he gets the chip. Once/If he does, it'll get louder, but you won't care.
Sometimes, you just gotta say "Shump it" and move on.