Believe it or believe it not, weelittledrummer, Sinn Féin is not an extremist party.

The DUP are fundamentalist Christians with their own brand of Presbyterianism, and apparently will sing hymns at the drop of Big Ian's big hat.
(Smaller parties also catered for, I believe)
Not, thoug what you would call 'representative' in the wider scheme of things.

The reason most people your side of the sea have been puzzled over the years is largely down to the manner in which the 'situation' has been reported to you.