Please note that wild rabbits in North America are probably cottontails, and not European rabbits (Oryctolagus cuniculus). All domestic rabbits including pet rabbits are the latter. They cannot interbreed. If the wild rabbit looks brown with natural brownish coloring but otherwise rabbit-like in shape and proportions, it’s probably a cottontail. If it’s got longer ears or longer hind feet, it’s probably a hare, which would include jackrabbits, none of which can interbreed with European rabbits.
Having said that, there are feral populations of European rabbits in parts of North America from release of pet rabbits that have somehow survived. They are less likely in colder regions, which are cooler than the native range of the European rabbit.
I do agree that fleas and parasites can transfer between a wild rabbit and your pets, so letting them get in physical contact is not recommended.