I really don't know, not having lived there for 46 years. Something I would never think about, but I would not be surprised if that was the case some years ago.I would have hoped it no longer matters.
As for opting to play for the south, I think that any NI player who could get on the Irish team would jump at the chance. There would be a much better opportunity to get into a major competition. I think somebody got death threats a short while ago for opting for the south, but have no idea what religion he practiced.
There is not much on the internet, but I read one quote that said Catholics have always played for NI, the problem was the supporters who were almost exclusively Protestant. But there seems to have been major progress there, with NI fans now being recognized as among the best in Europe.
You may not be aware that in NI Catholics are much more interested in Gaelic games than in football. And I am sure it has changed now, but when I lived in NI, anyone who played Gaelic games was forbidden to attend non-Gaelic sports events, such as football matches. So it is not surprising that until recently, NI football fans were almost exclusively Protestant. And hardly surprising that NI Catholics that were not influenced by the Gaelic Associations chose to support the Irish Republic team.
Ideally, of course, there would be one Irish team, as in rugby, where religion has never been a factor. But a possible merger of the Irish and Northern Irish Fooball Associations into one body, is way, way over the horizon.
I didn't know Gaelic sports were popular among Catholics in NI.