Tested multiple times on new worlds without any other mods, issue seems to occur randomly to all sea bunnies whenever there is a fairly large amount of sea bunnies spawned in. Models revert to normal when closing out and reopening Minecraft, but will become vertical again after a short period of time.

Edit: Playing on the latest 1.20.1 version of this mod (crittersandcompanions-1.20.1-2.1.5.jar). Also, the natural spawn rate of the mob on it's own does seem to be enough to trigger this bug.

Same :(
Use my fork. It has less bugs, but you must build it yourself.