I worked as a marine conservation educator for 15 years. Here's what I can contribute to this discussion. Unless you know for certain that coral rock was collected sustainably, ie, already dead and collected on shore, don't buy, use or exploit any product containing coral. Living coral is under tremendous environmental pressures caused by human activity, from pollution, global warming [the seas are profoundly affected, by rising temperatures and bleaching]commercial fishing, ocean bottom mining and recreational indifference.
There are many types of coral, so appearance is not necessarily indicative of where it came from or how it was collected. Coral, as has been mentioned, can refer to the animal living in the exoskeletons they create, or the skeletal remains of their homes. Many reefs are made up of a combination of living and dead coral. Living coral often builds on the remains of old dead coral skeletons, which is why it should not be collected from the sea, where it forms the base of reefs and provides homes for many aquatic critters and plants. So,dead coral has purpose. Even coral that's washed up into shores will eventually be crushed by the forces of the ocean into sand, though modest collection of washed up coral rock doesn't seem problematical in the scheme of things.
In some places, such as South Florida, there are deposits of ancient seabeds well inland that are quarried for coral rock to be used for building and for other purposes. That coral provides no benefit to living aquatic organisms and in my opinion, is not much different than any other quarried rock. Nothing lives on or in it.
So, if a product contains crushed quarried coral rock, I don't see any logical objection to it's use.