Cats don't really carry lots of diseases. If the cats are well cared for neighbor cats, there's probably nothing to worry about unless you're pregnant or suffering from some form of immune deficiency. . Cats can asymptomatically carry the parasite that causes toxoplasmois. Most people have been exposed, had it, and never knew it. Only if you're pregnant or immunocompromised is it a problem. (You can also get it from eating rare venison, but I don't know if you can get it from deer poop.)
Hmmm, a quick google says that you can get toxoplasmosis from beef, pork, or lamb, too.