This is right up my alley........veterinary. Those fluid filled cysts contain immature tapeworms. They are an intermediate stage in the lifecycle of the parasite. Once the rabbit is consumed by a predator, say a dog or coyote, the tapeworm completes its next life stage and matures into an adult tapeworm in the dog/coyote's gut.
If you look closely, you can actually see the "head" of the immature tapeworm inside the bubble-like cyst. It is the white dot. Eating these can infest a human only if the rabbit is consumed fresh-raw. Cooking kills the tapeworm. Although I don't remember rabbit parasitology
class anymore, I would think that smoking/drying the meat would also kill the tapeworm, such as in making jerky. But I'm not sure.
The rabbit is safe to eat if thoroughly cooked. I would cut out visible cysts just because of the yuck factor. But be aware that there may be some that are small
enough to be unnoticed, so don't lick the blood off your fingers or sample a piece of raw liver after dressing out your rabbit. While most tapeworms are fairly host specific, humans have been found to be infected by an assortment of cross species parasites, including tapeworm.
As you noticed, the cysts are commonly located in the liver, but also other locations in the gut. At times they can be located in the muscle, unnoticed. Thus the need to cook the meat.