We just returned from our cruise March 25th. Stops included Costa Maya, Belize, and Cozemel.
We didn't experience any issues in Costa Maya or Belize. We didn't get off at Cozemel, simply because we wanted to stay on board to just relax and rest up? Both places we got off, we remained aware of our surroundings and visited the shops and attractions right there in the welcome villages. I made it known that we would not be traveling(walking, taxing, or riding outside the gates, for any reason.
Being former military, I did not want to put ourselves at risk of anything that could be confused through lost translations or being misinformed, in any way? There were no incidents or problems that we experienced.
I would advise other's to be cautious but no need to be concerned to the point that you miss out on visiting these places, just be aware of your surroundings and always keep your ship in eye sight, if possible. We also gave ourselves plenty of time for returning back to the ship no later than an hour or two before time to be back on board. Many things can come into play while trying to get back to the ship that could possibly cost you precious time that you may have not planned on.