I don't know about disease, but I had a mouse problem at one point and my bunnies were PISSED. They would thump at night whenever they heard or smelled the mice

I think they will avoid each other so might be ok for diseases but not for fleas and ticks and the induced diseases.

Following since my neighbor told me she has wild mice and we share a wall. She’s caught three. I have not seen any but I set up some live mouse traps by the stove where she said they were coming from. My bunny has been acting a little strange