The real test, as far as I'm concerned, is the adherence of a university's faculty to the Mandatum. Simply described, it's a public oath by a Catholic teacher in which he promises to teach orthodox Catholic doctrine. Almost the entire faculty of Georgetown refused to so promise. I find it hard to describe a university as Catholic if its faculty refuses to teach Catholicism to Catholics.
The more honest administration at Fordham University (New York's historic Jesuit university) formally decided to become "a secular university in the Jesuit tradition" rather than continuing the farce of describing itself as a Catholic, let alone a Jesuit, university.
The liberationist movement began among Marxists in South America during the 1950s. They had a hard time convincing the masses to become Communists because of the devout traditional Christianity of so many of the working people of SA. The answer was to create a Marxist version of Christianity known as "liberation theology". The movement was suspect as a Trojan horse from the very beginning - and when Castro banned the Church in 1962 the mask was ripped off. The "liberation theologians" were instrumental among the Sandinista movement, and liberationist priests were the most aggressive enemies of the Church when Ortega came to power.
There is a liberationist streak among some Franciscans, Dominicans and Jesuits as well as the Redemptorists - but the Maryknoll priests are the most compromised. There may be liberationists among the Redemptorists in Ireland - but most Catholic priests in Ireland truly want peace.
One of the reasons why socialism made such headway in the republican movement from the beginning is because the Church was perceived as not being sufficiently nationalistic (which, thank God, it wasn't then and isn't now), while the Left masqueraded in an exaggerated patriotism calculated to deceive Irishmen.
The simple fact is that while the Protestant Ulstermen are fighting the IRA in reality, in their minds they're fighting a far different foe. They imagine that if the Six Counties are integrated into the Republic they'll become oppressed second-class citizens of an Ireland ruled by devious Jesuitical agents of the diabolical Pope of Rome.
In reality there are tens of thousands of Protestants living in the Republic who are quite happy, prosperous and unmolested. If the 900,000 Protestants of NI became citizens of Eire they would automatically become, at ~30% of the population, the second-largest voting block in NI - and would be in greater control of their political future in the Republic than they are now as a tiny splinter of the UK vote.
If they joined the Republic they would deprive the IRA of every last reason for it to exist. The worst blow they could ever strike against Sinn Fein would be to unite Ireland and make Sinn Fein completely irrelevant.
Hardened political attitudes will never allow this to happen - but the fact is that the Protestants of NI have nothing to fear from a united Ireland and the IRA, amusingly enough, has plenty.
The percentage of Protestants in the RoI has fallen steadily from 10% to 3%. The percentage of non-Catholics in NI who call themselves Irish has fallen from 20% in the 1960s to 2% now. Unionists have the impression that the other Nationalist parties often seem to bend over backwards to accommodate SF/IRA
You quite right that unionists have little say in the UK but from the data above you can see that they are growing less fond of the RoI.