Absolutely it is NOT! Cunard has dining categories, not classes. Where you dine is based on your cabin. The entire ship otherwise is open to all passengers.
As time goes on, more and more people who post on these boards have never traveled on ships with classes, nor do they know what the experience is. I traveled on the Italian Line and French Line in the 70s and Cunard in the 80s when the QE2 was still a two-class ship. For example, on the Italian line there were three classes. This meant that there were three of everything, e.g. three dining rooms, three swimming pools, three lounges, three children's playrooms, separate seating in the theatre, etc. There were signs at the entrance to these areas saying "First (or Cabin) Class Passengers Only". All far removed from Cunard nowadays.