I just have a discussion about NI politics that I thought I'd put here: Why is it that there are no left-wing Unionist and right-wing republican parties in NI? Surely there must be at least some left-wing unionists and right-wingers who support a United Ireland? Or are the communities that polarized that they both are also purely on opposite ends of the political spectrum? (with only one centrist party that combines both of them in the middle)
The Alliance Party is in fact really the "left-wing unionist" party you're looking for - it receives few votes from Catholics. Political cleavages based on ethnicity rather than ideology are commoner than you might think - similar stark divides occur in places like Malaysia or South Africa, and to a much lesser extent even the US. The present ideological divide in NI is partially because Catholics are historically underprivileged and partially a relic of the old Home Rule controversy. "Left-wing" Unionists vote DUP (the more "working class" Unionist party) or Alliance, "right-wing" nationalists vote SDLP or occasionally cross sectarian lines (Enoch Powell was elected for the UUP in what's today a safe Sinn Fein seat - NI is the only place on earth where electing Enoch Powell in a landslide is a sign of moderation!).