Here's a good rule of thumb. . .
If you truly want to bring things on board (like food) that is also available on board, but already included in the cruise price, there's no problem. If you want to bring things on board (like booze) that they also sell on board, there may be various sorts of issues. It all boils down to simple economics. Bottom line, nobody gives the slightest hoot about smuggling pastries aboard, although I can't see why you'd bother. Coals to Newcastle.
I suppose you can carry liquor around with you if you'd care to. Obviously, nobody cares if you're moving around on the pool deck with a beer. Some people, myself included, think it's tacky to wander around the public rooms guzzling liquor, but as I'm sure many will tell me in reply, "Hey buddy, I paid my damn fare and I can do whatever I want."
And, let's face it, you pretty much can. Rules are seldom enforced, the bounds of poor taste are stretched more and more ever year, so it's perfectly fine to do pretty much whatever you want short of a felony.
It is in very poor taste to bring liquor from your room to one of the ship's bars and proceed to sit down and drink it. People are doing it more and more because, hey, why pay bar prices when you can smuggle your booze onboard, mix your drink in the room, then bring it to the bar where you can watch big screen TV?