The opening words of the charter of the United Nations, published in 1945, are, "We the peoples of the United Nations..."
Perhaps "We are the people..." was a modification of that? Other than that, it may possibly have come from some older religious statement such as "We are the people of God" or "!We are the people of Israel" or something similar.
I've heard this expression for over 50 years and always from Glasgow Rangers fans to taunt Celtic supporters. There was always more than a hint of religious bigotry attached.
I live in Glasgow and am sick to death hearing this. Yes its to taunt Celtic fans and dates back to the really harsh days when the fight on the park spilled over to fighting in the streets.
Although not many rangers fans can sing it now lol due the the teams lack of performance of late. Looks like they arent the people after all.