Oh man--I read every post here with deep shame! Now, to qualify, we have two four year olds and a three year old. We made a HUGE deal about table manners (we do regularly, but especially ramping up to the cruise). The kids were extremely polite to everyone from the bathroom attendant to the person who cleared our plates at Cabanas, saying "thank you for making our cruise special!" or "thank you for keeping the ship so clean!" That said, they ran to our stateroom EVERY TIME to check the fish extender because they were so excited despite our constant admonitions not to run. Parenting these three so close in age is like trying to herd cats. They mostly kept their voices down, but we did let them do the stairs by themselves to work out energy. For the most part, people seemed super tolerant and even amused at our mob scene, and yes, we were always trailing the kids trying to keep them calm. However, they weren't running at night, just after dinner or otherwise (we had the early seating).
One other point--I agree generally about the cells/lights at shows but the kids club also pages you with your cell in the wave app. So as soon as we sat down to a show, we'd get a text from the kids club saying "kid a wants to be picked up!" or "kid b has fallen asleep". As a responsible parent, you pretty much have to check the messages when you feel them come through or whatever, and getting up to check the message every time is also super inconvenient for everyone around you. Just something to think about.
I get why people feel like they are entitled to an adult experience on a
Disney Cruise, but I also think that the expectation that all of the kids around them will be marching like Mary Poppins is in the house is probably a bit foolhardy. We're packed on a ship with that markets primarily that the cruise is a kid-centered experience where parents can also relax. There will definitely be inconsiderate kids and parents, but do keep in mind that no one concealed the kid-centeredness of the cruise-- and expecting that everyone holds the same standards as you is not realistic.
I have a friend with one kid who does a great "make good choices" and "let's play the quiet game" thing. It works temporarily for sure, but long term, the good old "ONE. TWO. THREE." is what I rely on. I guess my point is that parenting isn't easy on vacation and kids, especially out of their routines and surrounded by constant stimulus, are a challenge to control. Not saying I don't try (and succeed).
Another related piece--we were on the cruise and joked that Disney makes it really hard to parent. If your kid starts pouting or crying that you're "making" them eat their vegetables first, someone gives them stickers to try to cheer them up, and reinforces the attention seeking bad behavior. It happens at Disney World too

Our girls were fighting in their double stroller and so a cast member came out and gave them both princess crowns. In Nemo's Reef, I sat right by that little slide and if either of the girls cut anyone in line, I made them sit with me and skip two turns, and I got looks from other parents like "that's cruel!" It's honestly hard to give the kids actual consequences there, and we tend to be super strict and have high expectations for the kids that they know about. But they're still going to want to run towards the fish extender to beat their twin to see if there are presents.