Hallo there!
Just out of curiosity, are there rivalries among the Space Marine chapters?
I don’t mean the usual «We Ultramarines are the best», «No, we Space Wolves are» and such statements but the real feuds, dislikes and (if possible) outright hatreds: the only grudge I can think of is between the Ultramarines and the Space Wolves indeed, just because the latter refused to adopt the Codex Astartes (but I ignore how far it extends as far as relationships between them both are concerned).
Are there any more?
The Ultramarines are revered by many of their successors, and enjoy friendly, paternalistic relationships with them, there's a (relatively) friendly 5 chapter Olympicsalike competition that I recall reading about in the last Space Marines Codex, and individual chapters can get on fairly well during broader conflicts, (the Raptors and Red Scorpions got on well during the Badab War, for example). The Unforgiven have an unusually close relationship, too.
)