Forgive me if I am missing something here, and please correct me if I am, but I don't have the impression that the Ents have any real quarrel with dwarves. They do seem to have a quarrel with axes, weapons that dwarves often carry. In my opinion, there is an estrangement of the two races because of the extreme difference of their preferred environments. Dwarves and Ents never had much interaction, so far as I know. The hesitancy showed in Fangorn regarding Gimli seems to be more closely related to his axe than anything else.
If I were to go a bit farther, I would probably say that any animosity between Ents and Dwarves is most likely a result of the Ents' close involvement with the Elves, who themselves were extranged from Dwarves. The Elves' influence could easily lead to a mistrust of those the Elves themselves mistrusted.
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