Cozumel specifically has a law against removing any meats, fruits, etc etc etc basically anything that is not "prepacked" from the factory.
They are trying to prevent the invasion of the Red Palm Mite. There are huge signs as you get off the ship.
Boxed cereal and candy bars etc are ok.
However, feeding the fish in Marine Preserves in Cozumel is also against the law.
I am not a marine biologist so I don't begin to understand all the "whys"...but I obey their laws for the same reason I would expect someone from Cozumel to obey our laws...even if they don't understand.