In this case you would understand me if I pronounced "ABBA" the Swedish way, so the IKEA scenario doesn't happen.
Not that I do say it that way when speaking English, just like I don't say my own name in the Swedish way.
But if "ABBA" had been named "ÄBBA"[1] (to be clear, that's not "A with an accent", that's a completely different letter) then I would pronounce it "ÄBBA". And it would be annoying. But at least other music fans are not employed by ABBA, so shrug, Mötley Crüe.
I would imagine that a Chinese person would be annoyed if they had to refer to their president as "Eks Eye" when speaking English.
Or do you mean the accents in the ABBA songs?
[1] which would be confusing, all else equal, because it would be pronounced like Ebba in Ebba Grön, another band.