Technically, “snuffles” isn’t a real disease. It is an umbrella term that describes the symptoms of an upper respiratory infection in rabbits. People typically associate it with Pasteurella. But an upper respiratory infection can be caused by all sorts of bacteria, not just Pasteurella. Yes, Pasteurella and other types of bacteria can be “contagious”. However, an upper respiratory infection isn’t usually contagious. This is because rabbits harbor lots of bacteria in their sinuses. Yes, they can pick it up from another rabbit, but that doesn’t mean they will become ill. The rabbit’s immune system keeps everything in check and no one bacteria is able to take over under normal conditions.
If the rabbit becomes stressed or something suppresses their immune system, then it can upset the balance. This lets one or more types of bacteria take over… and then you start seeing symptoms of an upper respiratory infection.
So… the short answer is that I don’t think you need to worry about your rabbit too much. And your dad should have his rabbit checked out because this is something that can usually be easily addressed with some antibiotics. Most can be cleared up with a broad-spectrum antibiotic. Some can be more stubborn though, so sometimes you have to try another if the first doesn’t work.