Now I live in Detroit, right on the border of Canada. And I can tell you religious affiliation is a nonissue there. (Of course the queen in fact is the queen of Canada. But let's not complicate things.) Do English Roman Catholics sing 'God Save the Queen' with everyone else? I know during the reign of the first Elizabeth Roman Catholicism was a big deal. In fact, it could result in death. But in the 19th century came the Catholic Emancipation Acts. So is it still a big deal?
Jim In reality I think people in the UK are more interested in the Netflix ‘The Crown’ than the real one. The royal family is part of the right-wing establishment and is mainly promoted or defended by them through the right wing controlled media, its all part of their nationalistic, jingoistic and ‘respect your betters’ propaganda they like to promote. With many on the left been in favour of downsizing or even getting rid of the institution. So, in modern Britain it is often a matter of you social and political outlook (rather than a religious one) that dictates your view of the monarchy. I’m a leftie and an atheist and the first thing that pops into my head when I hear ‘God save the queen’ is the Sex Pistols.
------ That depends on whether you're a 'Little englander' or not !!! - to me its no more than a funural dirge, I prefer this one !!!