I can’t speak for other cruise lines, but I can tell you from 5 cruises on Royal Caribbean, they are cool with divers. If the ship is big enough (Radiance Class or above, I think) they have Scuba equipment for sale in the Sea Trek booth (Mostly Sea Quest equipment last time I was there) and even offer Discover Scuba in the pool.
In the same breath, I will also say that unless it’s an scuba excursion offered by the cruise line itself (like on CocoCay or Labadee) it’s cheaper to book with the actual operator. My last cruise to the Bahamas, we didn’t book through the cruise line, we booked with Stuart Cove directly and saved money. Of course, you need to know who the operator is, or at least find out if the people you want to dive with do pick up at the Cruise Ship docks..
Hope this helps a little..
Dale