I get the impression that some people would like us to abolish the national anthem altogether.
I wouldn't say getting rid of the national anthem is a good idea* but I do think we can do better than what we've got! England doesn't have it's own national anthem at all as it just uses the same one as the United Kingdom which is surely slightly sub-optimal. Jerusalem would probably fit the bill fairly well, though Land of Hope and Glory might work quite well.
Plus I do think that God Save the Queen/King is just rubbish. I'm sorry but it is. It's little more than funeral dirge when it comes to the tune and I do think it's a fair cop that it is quite religious about a Christian god when it is quite likely that a plurality of Brits are non-religious and Christianity might be the most popular but is no longer the majority of people's belief. Census 2011 suggests that 59% of Brits are Christian whilst 25% have no religion. But surveys since then suggest that things have changed. For instance the British Social Attitudes survey suggested in 2018 that 52% had no religion and 38% were Christian. Is a national anthem features quite a lot of god really representative of it's people? Particularly when you add in those who worship a different god to the Christian one!
I'm not really fussed about the monarchy bit of the equation. We are still a monarchy (a constitutional one to be sure rather than absolute) and there isn't much evidence to suggest there's a strong groundswell of opinion that we should become a republic (though I do wonder how that will change when the Queen dies). Polling I think usually puts it somewhere between 60 - 70% in favour of keeping the monarchy with somewhere around 25% in favour of replacement.
But in any case my main complaint remains it's just such an awful tune. If anyone could find a more upbeat tune to set the existing (or slightly tweaked) lyrics to then that would at a stroke be a massive improvement.
*Do many people? There are certainly some happy clappy types who say we should all live in harmony as one big human bubble, but they're pretty fringe!