Fionn, the song you're thinking about is:

NATIONAL BROTHERHOOD WEEK
(Tom Lehrer)

Oh, the white folks hate the black folks,
And the black folks hate the white folks.
To hate all but the right folks
Is an old established rule.

But during National Brotherhood Week, National Brotherhood Week,
Lena Horne and Sheriff Clarke are dancing cheek to cheek.
It's fun to eulogize
The people you despise,
As long as you don't let 'em in your school.

Oh, the poor folks hate the rich folks,
And the rich folks hate the poor folks.
All of my folks hate all of your folks,
It's American as apple pie.

But during National Brotherhood Week, National Brotherhood Week,
New Yorkers love the Puerto Ricans 'cause it's very chic.
Step up and shake the hand
Of someone you can't stand.
You can tolerate him if you try.

Oh, the Protestants hate the Catholics,
And the Catholics hate the Protestants,
And the Hindus hate the Moslems,
And everybody hates the Jews.

But during National Brotherhood Week, National Brotherhood Week,
It's National Everyone-smile-at-one-another-hood Week.
Be nice to people who
Are inferior to you.
It's only for a week, so have no fear.
Be grateful that it doesn't last all year!