They were Irish, but the unionists agreed (along with Great Britain) that Ireland should be ruled by the King and be under British rule, and subsequently they all adopt the "British" sect of Christianity (Anglicanism).
No, and the situation was and still is a lot more complicated than that.
The relationship between Unionism and Protestantism and Nationalism and Catholicism was and still is much more grey than many realise. The current situation with Northern Ireland makes this appear much more dry-cut than it actually is because NI was set up on sectarian grounds. However, historically many, in fact the majority, of the prime movers in Irish nationalism have been from Anglican backgrounds that would naively be associated with Unionism.
Also, Irish Nationalism was contrary to Unionism, but a good number of prominent Nationalists had Monarchist tendencies too, such as the founder and leader of the original Sinn Fein, Arthur Griffith[1]. Republicanism was something that came out of the more militant strains of Nationalism, as represented by the Irish Republican Brotherhood, who infiltrated Sinn Fein to use it as a vehicle for their own aims.
Moreover, the vast majority of Irish Protestants have been Presbyterian, not Anglican. Anglicanism was the church of the Establishment, not the common people. Presbyterians, being Nonconformist, were subject to many of the discriminatory practices of the various penal laws, just as Catholics were, because they weren't Anglicans, albeit not to quite the same extent. Anglicanism was historically the church of the upper classes and parts of the middle class.
[1] Griffith wasn't technically what you'd call a Monarchist, but he wasn't a Republican either. He supported the idea of an independent Ireland under a dual monarchy with the United Kingdom.
> No, and the situation was and still is a lot more complicated than that.
The question was "Did they [Irish Protestants] really consider themselves "Irish", though?" and the answer is "yes".
> Moreover, the vast majority of Irish Protestants have been Presbyterian, not Anglican.
The Church of Ireland is (and has been in recent history) the second largest Christian "sect" (as I put it earlier) in Ireland after Roman Catholicism. The Church of Ireland follows Anglicanism.
Of course are many many complications to the entire subject but that wasn't the original question, I was referring to the national identification of the Protestant islanders during the time frame of Jensen's claims.
> The Church of Ireland is (and has been in recent history) the second largest Christian "sect" (as I put it earlier) in Ireland after Roman Catholicism. The Church of Ireland follows Anglicanism.
Yes, you're correct in that the CofI is slightly bigger than the Presbyterian churches. However, that's not my main point. What I was disagreeing with was your conflation of Unionism and Anglicanism, which is entirely incorrect.
In the United States, they tended to identify as "Scots-Irish", and had a much more established place in American society (for example, at least three Presidents that I know of were Scots-Irish in the 19th century).
Scots-Irish isn't quite the same thing. Those referred to as 'Scots-Irish' in the US are descendants of Scottish (largely) Presbyterian planters. People who adhere to Anglicanism generally wouldn't consider themselves or be considered 'Scots-Irish'.
About half of Irish (whole-Island) Protestants today are Presbyterians concentrated in the Ulster Plantation (Northern Ireland); those are absolutely the same ethnic group as the Scots-Irish, despite that label not being used in the UK.
Ulster Scots is a different thing than was they're referring to. Ulster Scots refers to (largely) Presbyterian descendants of Scottish planters who emigrated to the US. Adherents to the Anglican communion wouldn't necessarily consider themselves 'Ulster Scots'.
They were Irish, but the unionists agreed (along with Great Britain) that Ireland should be ruled by the King and be under British rule, and subsequently they all adopt the "British" sect of Christianity (Anglicanism).