There is security in Cozumel when you enter the pier and then again when you board the boat. You only need your passport (or photo ID and birth certificate) at the airport, embarkation of the ship, and when going through customs at debarkation. You won't need it at any port as long as you don't miss the boat.
Can you use a birth certificate to cruise to Cozumel?
In lieu of a passport, children are able to use a U.S. state-issued original or certified copy of their birth certificate (hospital certificates are not acceptable) or a Consular Report of Birth Abroad, or a Certificate of Naturalization as proof of citizenship for entry into the U.S. by land or by sea.
Do you need a passport to cruise to Cozumel?
Is it safe to get off cruise ship in Cozumel?
Cozumel is very safe for cruise passengers. The ports are guarded and very secure. Cozumel police take safety very seriously.
What happens if you get stuck at a cruise port without a passport?
You will have to go to the US Embassy in whatever country your stuck in and apply for an emergency passport.