I remember trying to get to the bottom of whether sticks/leaves of members of the Prunus family were toxic quite a while ago. I think I came to the conclusion that they were OK and knew also the FHB had confirmed this. I remain slightly wary though and will still choose other foods to feed in preference and of course there is so much else that can be fed.
I couldn't find the website that I used last time, but I've found this :
https://csuvth.colostate.edu/poisonous_plants/Plants/Details/29 What I think this is saying is that all members of the Prunus family contain cyanogenic glycosides. It also states that there is more of an issue with wilted leaves, which I clearly remember from last time I researched it. I think the key point though is the information about simple stomached animals:
"In simple stomached animals, including the horse, the acid pH of the stomach and the fact that horses do not have a lot of bacteria in their stomach's to breakdown the cyanogenic glycosides, means that they are not likely to develop cyanide poisoning from eating the leaves of cherries and apricots etc."
My understanding is that rabbits stomachs are very similar to that of horses. And this is presumably why FHB can be so definite in saying that Plum is OK.