Is it bad for a Protestant country like the UK to govern a Catholic country like Ireland or want to take back Ireland?

In Europe, we have the principle of circular democracy. So, in principle, neither the United Kingdom nor Ireland are governed by a religious party.

However, in practice, it would seem that the Ulster Unionist / Loyalist party, which is predominantly Protestant, is not interested in the unification of Ireland for essentially historical and religious reasons.
While the Republicans, mostly Catholics, want a reunified Ireland. However, Republicanism and Catholicism do not mix.