I cringe and feel awkward when I hear what I consider a "wrong" accent.
Sometimes, I think, I'm justified because it is a middle class Cheshire singer-songwiter singing about meeting his love on the Derbyshire Moors singing in(what sounds to me like) an American accent.

But it's my loss. The singer is happy. The rest of the audience is happy. I wish I could relax and enjoy it.

Other times I feel awkward but I'm just wrong.
There was a BBC radio drama recently and one actor had the most awful and peculiar Scottish accent.   Bad enough that I felt I needed to write to complain.
But I thought I'd better go with some evidence. It turned out that the play was set on Skye and the actor was born and bred in .... Skye.

Accents with one label can vary widely.
JC will probably concur that in Liverpool you can hear the word 'book' as 'bewk' or 'buch'(ch as in loch). Depends which estate your family lived.

I don't particularly like Ewan MacColl's Scottish accent but it was 'his' Scottish accent and I'm content he had enough immersion in Scottish accents that we should accept it as such.
And as JC said our own accent can change as we move round the world. I find it difficult to go on holiday without starting to talk in my version of the local accent. Same with singing songs I've heard and try to sing.
I try to start with an apology especially if there is someone in the audience with the genuine thing.