There already are oral vaccines? There's one for rabies that's been airdropped across the US for years now... however to be fair that one is a live attenuated virus.
Edit and FTA:
Oral vaccines against rotavirus, cholera and polio exist, so it’s a viable strategy.
In this case it's my understanding that they're using the yeast to "smuggle" the viral proteins through the stomach acid, and then when the yeast is digested in the intestines the body is exposed to the added viral proteins. So since you need live yeast you can have vaccine beer, but not vaccine bread.
That seems unlikely. The entire way it works is the yeast produces proteins that "look" like a virus to the immune system, causing a immune response. However that's the only part of of the virus in the yeast, there's nothing else that completes the virus. It's like... a steering wheel without a car, no matter how hard I mime swerving to run over a pedestrian nothing's gonna happen, because there is no car.
If the viral protein mutated it'd either A) still be recognized as a viral protein and generate immunity for a virus that doesn't exist, or B) generate a non-functional protein that the body would simply digest.