Honest answer:

I think you're over emphasizing the Irish culture. "Fighting Irish" is a sports monikers, nothing more. It isn't the University's motto or mission statement, and, to my knowledge, there has never been a purposeful emphasis on recruiting Irish heritage students (or players). As I said earlier, the "Irish" moniker didn't even come around until at least 60 years after the University was founded.

Now, the Catholic component, definitely. That is part of ND's culture, and the overwhelming majority of students are Catholic, though certainly not all. And back in the pre-cable TV and internet days, ND was "the" Catholic team that Catholic fans across the country supported, even if they had no direct personal connection.

But I don't think that's true any more though. It's far easier to follow other, smaller Catholic school teams (Gonzaga basketball, Boston College football, Dayton basketball, etc) than it used to be. ND used to have a monopoly on radio, and then early TV, thereby driving up fandom. That simply isn't true any more.

But in the grand scheme of things, I just don't see why it even matters? Players (and fans) adopt the sports moniker of the their teams all the time, despite no direct personal connection. The Utah team probably has very few, if any, Utes. The USC football team probably doesn't have too many Greeks on their roster.

You're just overthinking it. More than a century ago, ND got the nickname "the Fighting Irish" and no one is exactly sure when or how. People appropriate that now, really just based on tradition more than anything else. Sports teams need monikers, and ours was decided a real long time ago.

Personally, I am Irish and Catholic. But I can tell you, only the Catholic part of the two was relevant to my decision to attend the University.