I’d rather people were English, Irish, Scots, Welsh, Manx etc than some kind of colonial descriptor. It’s like identifying as Soviet.
Britain doesn’t even exist for most people in the world. As I pointed out.
There are plenty of UK people who don’t identify as British outside the church. See surveys above. Personal experience too. The church has few of them though Because it has few political rebels. As usual, the church is out of touch. Why? Is it run by UKIP? No, they don’t tow the line enough.
The most notable LDS politician in the UK is a Scot nat. No idea if he identifies as Brutish, some do, some don’t.
In the UK, I have heard members make republican statements. Never heard from the stand, which is odd as the BoM comes out against monarchy on several occasions.