I don't know a thing about diving Bonne Terre, but I have encountered all the other rules quoted above, and I saw the reason for them. No gloves and no cutting devices (knives) are common rules (laws, actually) in marine parks. They are there to discourage divers from manhandling and damaging the environment. The fine for using either in Grand Cayman can be huge.
No lights is a common rule in the proximity to overhead environments for people who are not properly trained for it. The purpose is to keep unqualified people from penetrating and getting lost.
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The "No Gloves" rule reminds me of a story related to the topic of this thread. I was diving in Belize in the summer, and the water was quite warm. A father and two teenage sons showed up for a day's diving, and I noted that they were wearing no exposure protection on their bodies, just a swimsuit and T-shirts. Then I saw them pulling on 5 mm gloves, and I thought, "What the...?" I didn't pay much attention to them at first during the dive, but later on I saw the reason: they all had no buoyancy or kicking skills whatsoever, and they used their hands to grasp the coral and pull their way around the reef. I tried to make some gestures to make them understand that I disapproved, but they had no clue what I meant. After the first dive, I talked to the DM about it. He said he had seen it and would talk to them about it before the second dive to make sure it didn't happen again. On the second dive I just watched and saw that the DM had not done a blessed thing. They still did the same thing, and the DM watched them without reaction as they did.
I wil admit now before asked that I did nothing myself, either.