They do in fact carry diseases. So you need to do EVERYTHING you can to keep them out. I made that mistake a few years ago with my chickens. Wild birds were getting into the feed and water and everywhere else. Within their first year of life, all my pullets turned up with MS, a mycoplasma bacteria that never goes away. I had sick chickens for a year till I got it under control. Respiratory and feet issues. And they are now carriers of this MS for the rest of their days. It all came from the wild birds getting into the chicken feed and water. I finally had to use a fine netting over their large run. Had like 1/2 inch squares. I got it at the hardware store. It is normally used for protecting plants. I had to string it up in pieces and it was a pain in the rump. LOL Sort of set up like a circus tent style. Finally got the little birds to stay out. I eventually built the chickens a new coop and run to do away with this netting. So do your best to keep them out.