You are correct. Modern revolt against British Rule began in the 18th century and led to the much later formation of the IRB and IRA (and a few others in between) had little to do with religion. The United Irishmen, of which Theobold Wolfe Tone was a founder member and Protestant, was a non sectarian organization that aimed to secure an equal representation of all the people of the Kingdom of Ireland in the national government.
As for the GAA, its Constitution states at para 1.12:
Anti-Sectarian/Anti-Racist The Association is Anti-Sectarian, Anti-Racist and committed to the principles of inclusion and diversity at all levels. Any conduct by deed, word, or gesture of sectarian or racist nature or which is contrary to the principles of inclusion and diversity against a player, official, spectator or anyone else, in the course of activities organised by the Association, shall be deemed to have discredited the Association.
The Fenians (aka IRB) emerged in the 19th century and were banned in Britain and its overseas territories. Nevertheless, they evolved in North America and there were numerous Fenian Brotherhood raids into British assets in Canada. Interestingly, the Rifle Brigade took part in operations in Canada against the Brotherhood between 1860s-70s. Many of the Fenians were US Civil War veterans. It was overtly sectarian primarily because, like all immigrants everywhere, the Irish tended to settle in like minded groups and there was a tendency for Protestant settlers, especially in Canada, to favour the Crown.
The animosity between Catholics and Protestants in Irish affairs had more to do with the way they treated each other, in war and in peace, rather than because of their different church's. Some accounts of the Irish Civil war c.1922-3 indicate that the Pro-treaty and Anti-treaty IRA committed the most brutal atrocities upon each other. There was little room for religion. Indeed, for years afterwards, and to the present day, the only place that one can be assured of 'forgetful politics' is on the field of play within the GAA where former enemies first started to speak to each other again after the civil war.
