I wonder what they do with the sewage from south hotels.
You don't want to know but I bet you can guess. As Gopbroek mentioned, it gets pumped down into the limestone where it works its way out and into the ocean as it is forcefully pumped down. A local Cozumel environmentalist was diving a limestone cave and came across an 8" PVC pipe that ran down through it and into the cave floor. He posted about it on local Coz social media. Where that pipe ended no one knows but a hole/reverse well had to be drilled from the surface down deep to place that pipe.
All of cozumel is noting but porous limestone... there is no topsoil or clay or sand or anything that can serve as a traditional septic field fed by a septic tank the likes of which most of us know. A large resort can blast and dig a big pit in the limestone and maybe line it to some extent and try to build a septic system but the amount of waste it would have to be able to take and pre-treat before flowing to a traditional drain field treat would probably equal an Olympic sized swimming pool. Then, after pre-treatment, there is no other place that can serve as a drain field for proper leaching and treatment through multiple substrates until it finally makes its way through 100'-200' or so after 100-200 years or so back to the deep water table where clean drinking water is drawn from. In my opinion the southern development and the pumping of that waste into the limestone is a massive problem.
With regard to cruise ships, the popular belief that cruise ships dump raw sewage near the coast or anywhere in the open ocean is false. However, the grey water that comes from sinks, showers, laundry and ship galleys can be legally discharged within 3 miles of land in the US but I'm not sure about other countries' legal distances from land are.
One thing I can personally attest to over the 20? years we've been diving Coz is the disturbance of the sea bed when these ships come into and depart from port. My wife and I commonly stay at the Casa Mexicana where we have watched this on a daily basis. The bow and stern thrusters get cranked up to push away from the dock and then the main propellers come online to start other maneuvers and the water goes from crystal clear blue to a muddy, stirred up mess of everything and that turns the water into a brown, muddy plume of stirred up sea floor debris that carries on and on until it settles somewhere.
Years ago there were seahorses all over the place in the sea grass just south of the single pier in downtown San Miguel. As construction started on adding another pier to the southern port and since then with more and bigger ships started docking there the seahorses vanished and have never come back. A DM friend of ours for almost 20 years explained why... Seahorses hang on to whatever they can and feed on the smallest of other sea life that drifts past them... If you stir up the clean and clear water with piles of sediment and debris from more and more ships coming and departing the seahorses can no longer spot and find what they need to eat in that cloud of endless suspended mess that keeps on traveling north on the current. What the seahorses thought should be tiny shrimp larva is just a piece of sediment stirred up. To make this something everyone can maybe understand, it's like trying to find a single shred of green lettuce in bucket filled with shredded green confetti all stirred up. It's impossible to do and that is why the seahorses departed the shallows and have hopefully moved elsewhere. I bet they will never be back in the shallows. Maybe with the absence of cruise ships for a year or so perhaps I will be surprised some day and see one in the shallows but I doubt it as they've been there, done that, and their offspring will stay deeper and further out where they were born.