This has been discussed in some length here. There is even a sticky on the main Mexico forum about this.
The upshot is that the local community has developed protocols to safely conduct guided cenote dives for experienced OW divers. The safety record is excellent, as long as the rules are strictly followed, but things can go very wrong very quickly when they are broken. The most important rule is that the group has to stay on the cavern line at all times. All incidents that I am aware of have involved leaving the line, either because the guide wanted to show something extra, or out of convenience when the line makes a 'detour', or when a diver swam off to explore on his own. Other rules include no more than four divers per guide, the guide has to be at least a dive master with full cave certification and must be sponsored by a local shop, and must use a full cave configuration for the dive. Every diver must carry at least one light and be equipped to share air, and an extensive dive briefing must be given. And any diver can call the dive at any time for any reason without repercussions. The cavern line itself also has to satisfy certain rules, most importantly, daylight must be visible at any time (even though it still gets very dark), cannot go through narrow passages where two divers wouldn't fit side-by side, and can never be too far (200ft I think, but I'm not sure) from open water. It is also usually a thick yellow rope that clearly distinguishes it from regular cave lines in the area.
When you go with a reputable guide who follows these rules and you have your buoyancy dialed in and are not claustrophobic, these cenote tours are a great way to experience a stunningly beautiful cave-like environment. And you may just come back for more and get cavern and cave trained...