In the United Kingdom general election 2017 in Northern Ireland, the Democratic Unionist Party (DUP) and Sinn Féin won all but one Northern Irish constituencies between them. The DUP is unionist and socially conservative, whereas Sinn Féin is Irish nationalist and socially progressive. The more moderate unionist party, the Ulster Unionist Party (UUP), is also on the right, whereas the more moderate nationalist party, the Social Democratic and Labour Party (SDLP) is centre-left.
It appears that all successful unionist parties are on the right, whereas all successful nationalist parties are on the left. There are small progressive unionist parties, such as the Progressive Unionist Party (PUP), but they're unsuccessful. As far as I'm aware, there doesn't even exist a right-wing pro-Irish-nationalism party in Northern Ireland.
Why is this division so stark? Suppose that I'm an Irish catholic who very much wants to see a united Ireland, but I am socially and fiscally conservative. Within the Republic of Ireland, I could vote for Fine Gael, but this party does not participate in Northern Ireland. Likewise, if I am socially liberal and want to see a strong welfare state, but also want to see Northern Ireland remain in the United Kingdom, there really isn't any party I would identify with.
Why is it that there are no right-wing pro-Irish-unification parties or (successful) left-wing pro-UK parties within Northern Ireland?
NB: There is some discussion of Fianna Fail to stand for elections in Northern Ireland in 2019 — I believe this is a centrist, pro-Irish unity party.