What was particularly notable about these two was not that they refrained from trying to take each other's heads off, but that they developed a deep and lasting friendship. This was very unusual, Tolkien says so, perhaps it was unique.

Why should this be so?

There seem to have been quite a number of factors in the make up, psychology if you like, of Elves and Dwarves which would lead to a lack of understanding and empathy between the two races.

First of all the Dwarves were literally "The children of a lesser god" created by Aule not Eru (though he subsequently adopted them). This alone might make for some suspicion of their nature by the Elves. As the Dwarves were created by what was a "specialist-god" the intrinsic nature of the Dwarves might be expected to show rather limited or extreme traits (which they do)- another reason for the Elves to find them incomprehensible.

The limited traits which would be likely to prejudice Elves would include their secretiveness about their language(s). The Elves who made very free with their speech to one and all (they called themselves The Speakers (Quendi)) must have been baffled by the Dwarves reticence.
The issue of secrecy affects the Dwarves' strange lack of evident females. Secretiveness does not promote understanding or trust between peoples.

Also the material aquisitiveness of the Dwarves must have led to Elves distrusting them. Sharp trading practice does not lead to mutual esteem.

The Dwarves appear to have lacked an appreciation of music, or it was grossly different from that of Elves or Men, this would have been something which would not endear them to the Elves.

The Dwarves were in general monomaniacal, building, creating objects of craftsmanship and amassing worldly wealth were the things which chiefly mattered to Dwarves. These drives were much less important to most Elves.

In general Elves were aware of the natural environment and their creations (buildings, jewelry etc.) were made to harmonise with nature, the Dwarves in contrast seem to have delighted in overcoming nature and imposing their will on it.

All in all it is not surprising that a basic level of distrust and lack of sympathy existed between the two races. Any actual hostilities between them due to specific grievances would only tend to reinforce prejudice.