"British" doesn't really come into it. The one thing that will unite Rangers type Protestant Scots and Celtic type largely Irish descended Catholic Scots for a short spell will be backing Scotland to knock England out of the World Cup in a few days.And they won't be standing to attention when the band plays God Save the Queen, which theoretically is the "British" national anthem.

The Fields of Athenry has come to be a tribal Anthem for Celtic supporters, that's enough reason for Rangers fans to see red (or maybe orange) when it's sung. The words don't have much to do with it.
Not unusual, when you think of it. I mean what have the words of Dixie or Waltzing Matilda got to do with the emotions they link to?

And when it comes to Football... there are places you could get kicked to death for singing "I'm for ever blowing bubbles".