Our last several cruises have been split between RCI and Carnival. I purposely did a couple of RCI cruises solely to get diamond status, although one of them was also doing the Alaska itinerary we wanted. Since this also gives us Elite membership on Celebrity, I can say that I will tend to look first at RCI and Celebrity before the other lines. Our Carnival cruises have mostly been swayed by the convenience of driving instead of flying. However Carnival has won us over as being a really good cruise line too and I am certainly willing to fly to cruise with them. But if NCL had been in Mobile I could easily tell you I had many NCL cruises instead of just two of them.
I enjoyed our Princess cruises and it has been a few years so I might look at them for next year.
To answer the question: I do have some loyalty to the Royal Caribbean brands since we like RCI and Celebrity. But it depends on the itinerary. Caribbean? I'll be on RCI or Carnival. The Caribbean itineraries don't matter that much to me. Alaska or Europe? It's all about the itinerary and the ship is just the conveyance. I'll go itinerary, then cruise line, then ship for those two places.