You're NOT in EPCOT anymore!!!
Lots of the rest of the world is much different than what we are used to here in the USA
There are armed military / police patrolling the port areas and the nearby cities in many non USA countries (except for many of the Caribbean islands - or I've gotten so used to seeing them that they don't bother me any longer)
Mexico - yep they are visible and out in force.
London, Italy & France - they are there, just not as obvious - unless you are near a "target" (ie: Eiffel Tower)
Turkey and Egypt - Pre "Revolution" - they were on the streets, in the venues we visited and we had our own on the bus with us.
Barcelona - I didn't really notice them there - but a long time ago in Spain while Franco was still alive - I witnessed numerous "shows of force" in the areas of Spain that I was visiting.
Sorry, that probably didn't help!!
Never felt Unsafe in Cozumel or Playa del Carmen (mainland). We were just there a few weeks ago - we chose not to get off of the ship because we expected the weather to be a bit windy and cool and we would have been at a beach / in the ocean. We stayed on the ship and had a great time with an empty ship and glorious weather!! Our tablemates and other people we talked to had a great time on excursions or on their own in Coz'