The thing to understand here is that, in Northern Ireland, "Catholic" and "Protestant" are primarily ethnic and cultural labels, rather than religious ones. The Troubles was an ethno-nationalist conflict, rather than a religious one. It wasn't a conflict between two groups of Christians so much as a conflict between two ethnic groups who held different national identities and who happened (for various historical reasons) to have been labelled with religious terms.

So, to your question. There's a well-known joke in Northern Ireland about a Jew being asked if he's Catholic or Protestant. "Neither, I'm a Jew", he says. "Well are you a Catholic Jew or a Protestant Jew?". Now, like I say, this is a joke. But, like many jokes and especially those which are satirising politics or culture, it contains a kernel of truth.

Northern Irish society was (and in many ways still is) heavily divided between two ethnic groups. Members of those ethnic groups were, for many decades, heavily armed and waging a war not only against each other but also against the state (and at times with the support of the state - things got messy). The armed members of these ethnic groups were immensely powerful and largely controlled sizeable areas of (particularly urban) territory. And the unarmed members of these groups were naturally rather suspicious of outsiders.

Northern Ireland actually has a very small non-Christian population. As of the 2011 census it was less than 1% of the population, or about 15,000 people (not taking into account those with no religion). As a matter of expediency, and unless you happened to live in the wealthier parts of Belfast which were less divided and didn't come under paramilitary control (although paramilitaries were still active), it would have been wise in the extreme to align yourself politically and culturally with whatever ethnic group was dominant in the area in which you lived and worked. Not doing so could have grave consequences, up to and including death, just as it could for anyone of any faith (Christian or otherwise) in a similar situation.

So if you were a Jew in Northern Ireland during the Troubles and someone asked if you were a Protestant Jew or a Catholic Jew, the safest thing to do would have been to check whether the area you're in was flying the Union Jack or the Irish Tricolour and profess a deeply held belief accordingly.