Getting off your cruise ship in Mahogany Bay

We are leaving on the Carnival Dream this Sunday - and Mahogany Bay is one of our Ports.

We are traveling with our 4 kids and I was wondering if I am allowed to take snacks that we have, off of the ship. When we cruised to Cozumel in April we saw that there was a check point and they were going through bags and throwing out food. I wasn't sure if this was standard policy in every port or not.

My 3 boys want to snack/eat all of the time. :(