It is remarkable how much the Queen's standing has improved during the time since that song (1977). My (UK) family are (as far as I know) staunch republicans, but the last couple of decades have seen all of us soften our disgust with the monarchy as Elizabeth represented it. We might still want the whole concept destroyed, but there is nothing close to the vehemence of Johnny Rotten (Lydon)'s lyrics from that song.
Nevertheless, that is how a bunch of people felt in 1977, and as our memories become even more gilded and rose goggled now that she has died, it may be worth remembering those feelings too:
God save the queen / The fascist regime / They made you a moron / A potential H bomb / God save the queen / She's not a human being / and There's no future / And England's dreaming
These days, I think even us staunch republicans/anti-monarchists would begrudgingly admit that "She could have been worse" and that she actually was a human being.
Maybe Charles will have the guts to end it all, but it doesn't seem likely.
In the 90s (the only era I can remember) things were quite different too: there was the whole hubub about Camilla who was (IMO unfairly) extensively vilified in the media, had private telephone conversations with Charles were leaked. I'm not sure that would happen today; or if it did, it would get considerably less attention. Then there was the whole bruhaha about Andrew and Fergie, and let's not even start about Diana.
Maybe today Kim Kardashian or whatnot have taken the place for the "gossip inclined". Or maybe I just don't pay as much attention to these things as I did back in the day. But it seems like reporting is completely different.
As for punk: that's basically intended to offend innit? I'm not sure if you can really tell the general mood of the country from punk.