Well, I've gotta say, I have about a dozen each of Flemish Giant rabbits and mixed hens (mostly Buckeye's). They all "free range" in the backyard and the rabbits seem to prefer the chicken feed over their own. We supply plenty of hay and they still go over to the chicken feed. The chickens and the rabbits were eating ALL the food....dog food too (yep the dog's are out with them and have never harmed any animals) and the rabbit food. The dogs are black labs by the way.
Probably for another thread, but I found that if I bring home a new animal (chicken, rabbit, whatever) if I keep it caged for about a week and allow the dogs to get used to the sight and scent of the animal, they don't bother them once they're out and free ranging.
I bought an automatic chicken feeder to fix the "problem" and the rabbits figured it out faster than the chickens did. Raised it up and they still get to it.....now I'm gonna try putting a small roost in front that the rabbits won't be able to stand on, but I don't think that'll cure the problem either...they're pretty crafty. I'm not too concerned. I eventually bought an automatic dog feeder to keep the chickens out of that.....we'll see if that works....I think it will, it's raised off the ground so I don't think they'll be able to access it.
We eat the rabbits but use the chickens only for eggs.....never had any problems with illness, flavor, or otherwise.
The rabbits and the cats (outdoor assassins) also tend to periodically go into the chicken coop for a nap.....it's actually pretty cool how they all get along.
I'm not into miniature factory farming so I'll do what I can, but I'm not gonna sweat it if they keep sharing their food.
This may not be what a "vet" recommends, but since they've never gotten sick, it seems they know what they can and can't/shouldn't eat.
So far, so good.