I don’t mind coming to Coz in July, though for me a July stay means that access to a REAL swimming pool is an absolute necessity. That means that Casa Mexicana, Suites Bahia and Suites Colonial, places I would very gladly book for a December or January stay, are crossed off my list of acceptable hotels. I’ll go to Hotel Cozumel, with it’s HUGE swimming pool, or Casa Del Mar (ground floor garden level superior room, so I can walk out my patio door to the pool). Hotels without good AC are definitely out of the question. July is hot and humid, so be ready to sweat. A LOT. That also means that slightly less thermal protection when diving is OK, and there is no chance of getting chilled on the boat rides after diving. And there are smaller crowds, less noise, better deals.
PS. That also means a higher taxi budget for me. While I don’t mind the walk from Hotel Cozumel to downtown, or even the long hike from Casa Del Mar, during most of the year, in July I can’t make those walks without being a dripping wet mess by the end, so I’ll take a cab more often.