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.

It's funny that you specifically mentioned the '60s, because back then they were pretty routinely administering the oral polio vaccine on a sugar cube for school children

That's how my dad got it back then