If you will allow me to make some comments as someone who has worked on cruise ships...
It does not matter to the staff if you are new or not, when you see new people coming on board every week you start each cruise with an open mind and you see where things go. 90% of the time you are just doing your job exactly as you would every other cruise. To me it was all one long cruise, not a series of cruises in a row.
You meet new people all the time, not just on the first day of a cruise, but by about the third day of a cruise you recognize the "feel" of the cruise in progress. They all feel different for different reasons. Sometimes is who is booked, how the weather affests their mood, whatever, but you definitely sense a difference in every crowd you have.
The guests meet and interact with you based on your personality. Now, unseasoned cruisers seem to be having more fun and everything is new and wonderful to them. They are often more fun, but they are more prone to "crises," too, because they don't always know how to do things.
Seasoned cruisers always have higher expectations, but that doesn't mean they are always more demanding. Sometimes they are less demanding because they are familiar enough with cruising not to get upset by little things (unfamiliarity with a new thing often causes a lot of unnecessary anxiety).
That being said, it is an individual thing. You can't stereotype cruisers behavior.
Now - IF a frequent cruiser acts like the rules don't apply to him it is because somewhere along the line he has been given special favors by a staff member he has befriended. It is like training a puppy, if you spoil them they will learn bad behavior. It isn't the server's fault, just like people who love their puppies they are just try to give them some special attention, but sometimes it has the wrong result.
When frequent cruisers get spoiled it manifests in their relationship with service people. If they feel buddy buddy with the hotel manager (for example) they also feel like they are running the place. When that happens they forget they are passengers, expect more and tip less.
Cruise lines love all passengers. Most experienced passengers are great guests who usually tip well because they know how the system works. But that is different from a person who takes the same ship over and over. But anyone who cruises three or fourt imes a year will be considered important even if they are a pain in the keister.
Yes, crewpeople change on ships, and to the frequent one-ship repeater that alone makes them feel somewhat superior. They probably tell waiters "that isn't how they do things on this ship." That is probably what the servers the OP spoke to were referring to.