Well, it looks as if the only really bad thing the Elves did to the Dwarves was to hunt Petty Dwarves before they understood that the Dwarves were sentient, and make war on the Dwarves when they killed Thingol and took the Necklace.
And it looks as if the only really bad things the Dwarves did was to kill Thingol and steal the Nauglamír (the Necklace of the Dwarves) set with the Silmaril, then sack the city of Doriath when the Elves retaliated.
My point here is that long after those events, the Dwarves and the Elves had friendly enough relations to trade fairly extensively, and for Celebrimbor and/or the other Elven Smiths to give seven rings to the Dwarven Kings. Yeah, the Elves kinda-sorta blamed the Dwarves for awakening Durin’s Bane, and Tharanduil did throw Thorin and his party into prison. But really, the relationship by that point was more like that of the English and the French: both on the same side and willing to trade for mutual benefit, but not really loving one another all that much. I’m not sure it constitutes a rift.
The Dwarves were always a very insular, secretive people, so that the only Dwarves we ever see are craftsmen and warriors. By the Third Age, the Elves had become very insular and secretive as well. The Elves of the Third Age are kind of faded: not as heroic or studly as they were in the First Age, but also much less driven by their passions, so that you no longer would see a Kinslaying or any of the other great crimes committed by some Elves in the First Age. Maybe they just became too tired, too detached. You would never see Elves of at least the late Third Age waking up trees and teaching them to speak. They had withdrawn into themselves.
So the Dwarves didn’t trust the Elves because they had some bad history, but mostly because they didn’t trust outsiders at all. And the same holds true for Elves. Both races felt pretty comfortable with Hobbits because they didn’t feel at all threatened by them. Dwarves had lived among Men long enough that some of the rough edges had rubbed off, but you still didn’t see Dwarves really trusting Men. And Elves trusted only the Numenorians among Men, and even there they weren’t any too sure (and with good reason).
So I think the rift, such as it was, was born of bad history on both sides contributing to the natural secretiveness and distrust for the Other that both races had by the end of the Third Age. As for the fault wrt the bad history, there’s plenty of blame to go around. I suspect that the Elves rather looked down their noses at the Dwarves, while hiring them to do their literally dirty work (mining and crafting), and I’m sure that rubbed the Dwarves very raw.
But what the Dwarves did was very wrong. The theft of the Necklace and the slaying of Thingol could be attributed to a few bad apples, but they sacked Doriath, and that’s very bad. I don’t see the Elves having done anything quite as bad as that to the Dwarves. You can say that the Elves should have known better, but the fact is, the First Age Elves were very much ruled by their passions, and sitting at the feet of Power doesn’t seem to have changed them significantly for the better. By the Third Age, the Elves had calmed down a lot, but with what appears to be wisdom also came passivity.
Now, please explain to me why I’m wrong, because frankly I don’t know what I’m talking about.