IIRC, there would be a big communal jar and a group of people would stick long reed straws into it. Which sounds super gross, but alcohol would kill the germs? Maybe?

That plus (or because?) humans were facing totally different germs.

Not reed straws; oversized clay ones, and after you used it you'd snap off the bit you used so the next person could have a go. Archaeologists have found tens of millions of straw pieces in middens

Communal cups (big, ceremonial and normal version) were also big in the ancient world in general. You’d get invited to a party and a cup would get passed around or host and guest would share a cup as a mark of respect.