Where I live, some sugary food left out, even for a few minutes, will have ants swarming over it in no time.
When people are freaked out by harmless insects, there's usually little point in trying to get them to understand or acknowledge that they really aren't being reasonable, because it's a personal phobia.
That said, ants aren't harmful (yes, some sting, but the sting dissipates quickly), they don't carry disease, it won't hurt you in the least to ingest them, and if you clean up well after preparing food and don't leave out anything that will attract them, they'll go away. They move out of an area as fast as they move in.
But if you simply can't bear to stay there, I guess it's something you'll have to work out with the host. Just remember that the host didn't leave donuts out on the counter overnight, you did. That isn't the host's fault.
@Brandi105