We did it last December and didn't have a good experience. I've read a lot of people who had the opposite, so my review is just one data point and may be an aberration.
Firstly though -- if your main concern is that the animals could be dangerous, I did not see any reason to be concerned there. They seemed very docile to me and used to people being around, for better or worse. I saw nothing that indicated the animals themselves are a danger and never felt in danger from them.
My family and I did not have a great experience in our excursion for other reasons. The boat that was supposed to take us there broke down and we ended up having to wait a very long time until a new boat arrived -- so again, probably atypical there. When we got there, the water was very rough (I do not know if that is typical or not -- the weather was otherwise excellent) and the place was crazy crowded, to the point that my kids wanted to get back on the boat within a minute or two of getting off, and where if I stuck my head under water, I had to worry about getting kicked in the face. I found some of the other boat captains / tour guides to be quite rude (i.e. I had one yell at me because he picked up a stingray to show his tour group and I happened to be standing nearby when he did it... and I guess since I was not on his boat I was not supposed to see it.. or something). The trip there and back was about as long as the actual time spent at Stingray City.
So overall for us, it was just not worth it. It was by far the lowlight of our cruise and not worth the money. But again -- I have read a lot of people who had very different experiences, so ours may have just been a confluence of bad luck, as sometimes happens.