Certainly a lot of segregation going on with Celebrity reputed to be one of the worst (1st and last Celebrity cruise was on the Millennium before it was configured for such). You can certainly tell on the menu (3 different dining rooms for the various cabin classes - no pay option available) and there's also reserved seating for the showroom. A bit more "in your face" than, for example, NCL Haven, MSC Yacht Club. Cunard certainly has class segregation (re: access to various areas) largely depending on whether you are in "grill" class or not.

Not saying it's right or wrong as I guess it's largely dependent on whether one wants to be treated like royalty or like a steerage passenger. My take is not to patronise the cruisecos whose segregation policies you don't agree with.