Depends on the type of fungus, fungal infections from birds, bars, and the ground are quite serious infections, and often require toxic anti fungal to kill it. If you heard amphotericin B, it's used to treat lethal fungal infections, but it's a toxic agent. Candida can be quite serious in immunocompromised people, but is was originally often found in people with hiv. Mammals were quite smaller and they could survive on less food, plus their niche was mostly small or nocturnal insects around the time of the dinosaurs, and most insect and plant orders survived the extinction event.
Bats themselves are mysterious as they don't know when they evolved, or what animal they came from. Just like bed bugs which came from bats, but nobody knows where their origins came from