The paramilitary organisations did not hold particular theological positions and members were not, in general, especially pious. They were, for the most part, members or adherents of their respective churches. For Protestants this was mainly Presbyterian and Anglican. Religious background, as a proof of allegiance and a guard against infiltration, was more important than personal faith or religious practice. Church leaders of all denominations condemned paramilitary violence.
The conflict was between two communities who defined themselves, and each other, as Protestant and Catholic, hence the use of these words to describe them. To suggest a dichotomy between "Irish" and "British" would have been highly controversial.
There were particular theological/biblical motifs resonant in the wider Protestant community. There was an understanding of themselves as part of God's chosen people in a way Roman Catholics were not. Loyalty to the Protestant Queen, Elizabeth II, was a religious imperative and to be contrasted with loyalty to the Pope. The UVF (a Protestant paramilitary group) had its motto "For God and Ulster"; while the UDA (the other main Protestant one) had "Quis Separabit" - meaning "who shall seaparate us?". This is from Romans 8, 35 "who shall separate us from the love of Christ" but was taken as meaning who shall separate Northern Ireland from Great Britain. The number two and a half was regarded as symbolic, and this referred to two of the tribes of Israel: Reuben and Gad, and the half-tribe Manasseh. These two and a half tribes did not live with the other tribes on the West side of the Jordan, but remained on the East side. Nevertheless they were in every way as much a part of Israel as the other tribes. In this way Northern Irish Protestants, though separated by water from their co-religionists in Great Britain, were no less British than Gadites were less Israelite.
A frequent motif on Northern Irish Protestant banners is that of Ruth the Moabitess with a text from Ruth 1, 16 "Intreat me not to leave thee, or to return from following after thee: for whither thou goest, I will go; and where thou lodgest, I will lodge: thy people shall be my people, and thy God my God." This is taken as symbolising the loyalty of Northern Ireland to Great Britain, even if Great Britain were, like Naomi, to urge Northern Ireland to go back.
A much more common motif is that of King William III who defeated James II (and VII of Scotland) in Ireland in 1690, settling the Glorious Revolution and Protestant monarchy for the whole British Isles. William was James' son-in-law, just as David was Saul's. Saul lost God's favour and was replaced by David and in the same way, James by his Catholicism was held to have lost God's favour. This gives another theological/biblical facet to Protestant understanding of the conflict, as part of a centuries long dispute with biblical parallels.
One reason for the predominance of Catholicism in most rural parts of Ireland was the bungling of the Reformation. The reformers believed liturgy and scripture should be in the language of the people and in England many accepted this had advantages. In Ireland the authorities in Dublin wanted to spread the English language amongst the Gaelic speaking rural areas, and so initially introduced liturgy in English. In trying to do two things at once, they accomplished neither. The reformation was rejected by the ordinary people. This may explain the questioner's reference to Catholic as synonymous with "Irish".