I keep wondering whether I should change my lone "Don't care" vote...
My initial reaction as a potential passenger is that it will make very little difference to the service and quality on board whether these ships are registered in the UK or elsewhere. I am pretty sure that Cunard will continue to strive to maintain that superficially "British" atmosphere they have created for these ships, and will also make sure that several of the highly visible officers and crew willl speak with an impeccably British accent.
The place written on her stern is not hugely important to me, as I have no strong attachments to Southampton as a city. I did a little bit of internet surfing last night, to check out the other "British" cruise lines, and found that all of those I have enjoyed or am tempted to try, i.e. Fred Olsen, CMV and Saga, have registered their ships outside the UK and mostly outside the European Union. The major German and French cruise lines seem to have done the same thing. Costa and HAL retain some European registrations. Yet all these lines seem to be able to create something of the atmosphere of their so-called "home" countries (UK, Germany, France, etc.) onboard. So, I would not be overly concerned that the "British" (still in inverted commas) atmosphere of the Cunard ships will be lost, just because of the change in registration.
The reason why finally I DO care, is because this change in registration will most probably erode the working conditions of the non British crew members on board, who will no longer be protected by equal treatment legislation. I know from observation, as well as many conversations, that they work very hard, spend most months of the year away from their families, and have the great objective of succeeding as the main breadwinner of an extended family, including most importantly those they wish to provide with a good education so as to improve their life chances. In other words, those who need a decent income most, will now receive less. Those who are already at the bottom of the salary scale on the ships, can be pushed back a little more.
So, for myself, I really don't care about the port of registration -- but because of the real reasons for this change, I care deeply.