Except for one port, I have never taken my passport ashore. Have taken a photocopy and my driver's license.
The exception was on the Med Repo cruise. We had a stop in Gibralter. Which a photocopy would have been fine, but the excursion was going into Spain, so we might have needed it at the border crossing.
Seems like Disney made it clear that we needed the real thing on that excursion.
You may want to check with Guest Services when you get onboard and they will tell you what you would need. If you haven't made a copy of your passport, they will do it for you.