I don't know much about keeping rabbits, but I do know that they are herbivores, while chickens are omnivores, so I assume their pellets contain more protein and calcium than would be healthy for a rabbit.
Years ago when I had both, the chicken feed and the rabbit feed both had about 18% to 20% protein (that was rabbit feed suitable for pregnant does and growing bunnies, chicken feed for laying hens or for growing chicks.)
Most chicken foods seem to have only plant products now, with no animal protein. The protein levels seem to be lower now than what I used to get, too.
Chicken feed is mostly based on grain, and rabbit feed is mostly based on hay, so that is one difference. Layer feed also has much more calcium than a rabbit needs.
I'm pretty sure a few bites of each other's food won't hurt either one, but I don't think either would do well on a constant diet of the food meant for the other species. If someone put out a container of each kind of food, I think the chickens would mostly eat the right food and do fine, but I'm not sure if the rabbit would make wise choices.
Another reason to house them separately is that chickens generate a lot of dust, and rabbits are quite sensitive to air quality.
What worked well for me in the past was rabbit hutches inside a fenced yard, and that yard was also the chicken run. Plenty of fresh air for the rabbits, neither animal could bother the others, and the chickens could scratch around under the rabbit cages. They found worms and bits of dropped rabbit food (they wouldn't eat much rabbit food, but seem to like a few bits here and there by way of variety.)