Apparently, the main antagonist team (always presented as honorable antagonists and models of sportsmanship) in this anime is the Ojo White Knights. They’ve got plenty of good players and know what they’re doing.
In episode 4, we visit their high school. But it’s not some big city high school, and it’s not just another private school for rich Japanese kids. Noooo, it’s a private Catholic high school!
In Japanese pop culture, Catholic high schools have a cachet to them. One gathers that when they were originally allowed to be founded, they quickly got a lot of rich non-Catholic students because they taught Western knowledge. Often, graduates were influential. Often, their families go to the same school for generations.
But usually, in anime, Catholic high schools are only used for their look or a touch of exoticism and haut ton. When you add in the uniquely Japanese bits of Catholic school culture to the anime writers’ imaginations (sometimes pretty fevered, when it comes to Catholic schoolgirls), a US Catholic doesn’t usually see anything too recognizable. I mean, did you have a lot of random stained glass windows in your parochial school? Heck, no.
However, the Ojo White Knights apparently think they are Notre Dame. Heck, Ojo Private Senior High School was apparently designed to look like it’s a certain campus in South Bend. (Which could happen, especially in Japan.) They wear Irish circle-crosses on their workout gear. They have a big banner on the wall that says “Glory on the Kingdom”, which sounds like the anime writers are trying to do AMDG in a way non-Catholic Japanese would understand. So the ridiculously huge number of stained glass windows, I’m ready to overlook. 
So far, there’s no indication whether the characters are Catholics or not (or at least, none recognizable to me as a non-Japanese!). If there’s more Catholic culture in it, I’ll let you know. But given how weirdly that Christian stuff can get mutated by non-Christian Japanese, it’s probably just as well if we don’t see any attempt at depicting a pre-game Mass. 
I have sudden images of Saints intervening directly in the games when called on…. talk about intercession!
If you watch episode 9 of Code Geass R2, the Brittanian bishop at Empress Tian Zi’s wedding is vested in Epitrachelion and Phelonion. With Mitre too.
Oh, I believe it. Whenever there’s a chance to show pageantry, stuff gets dumped in. (Of course, this is exactly what a lot of Western directors think all historical flicks should look like.)
But of course, with something like Code Geass, they could easily have some really complicated backstory to explain this. Or it could just be that Canterbury decided that Greek vestments were trendy.
I forgot to mention another point. Just as our heroes go to Deimon and their team is named the Devil Bats as a pun on that, “Ojo” sounds like “Ojou” (female master, lady). So it’s a total Our Lady/Notre Dame thing going on.