As you seen in Ocarina of Time, the world of Hyrule was created by the three goddesses. Since this creation story is known to be actual fact, this means that any real world religions seen in the game are in fact wrong (in this world). I suppose there's a small chance that this could be a little off-putting for any devout followers of a real life religion who happen to be fans of the series, but, I don't think anybody has a real reason to be offended, it's not like anybody's making a serious argument about this.
It is Christianity which is the religion that appears most frequently in The Legend of Zelda. In the very first game, one of the items you can obtain is called the Book of Magic, which, when you look at it, clearly has a crucifix on the cover and was even called a Bible in the original Japanese. In the second game, you can find a building which is very clearly a church, as well. In fact, the version of Link in these two games is probably a Christian himself since he clearly has a cross on his shield. So, it's quite clear, that, by this point in the history of Hyrule, Christianity is pretty well established. What's especially interesting is that Christianity seems most prevalent in Hyrule during, what The Hyrule Historia calls, 'The Era of Decline'.
But, actually, Christianity must have existed in Hyrule almost since the very start. In Ocarina of Time (which is, chronologically, one of the first games), while it has been removed from all recent versions of the game, originally, when you went into the Fire Temple you could hear Islamic chanting in the background, which means then, that Islam must exist in Hyrule. Knowing what I do about Islam, it seems to be impossible that there is anyway it could have come to exist BEFORE Christianity and so you must also assume that, by that point in the history of Hyrule, that Christianity did exist but that it simply wasn't seen.
What I find interesting, is that, when you see all of the strange creatures that live in Hyrule (Octoroks, Zoras and Koroks for example) and you look at the unusual geography such as islands that float in the sky, you can only really conclude that The Legend of Zelda series does not take place on Earth at all. But, since the Bible exists in Hyrule, it must take place on Earth since the Bible contains references to various real life geographical locations. Is Hyrule then, actually supposed to be set in our reality, but in an entirely lost civilisation?
You could even say that the Christianity in Hyrule actually has its roots in the truth: the three goddesses who created the universe could have become, over the ages, the three aspects of the Holy Trinity. The Christianity in The Legend of Zelda could have started as the true religion of the world, but over the years slowly become corrupted by people and lost most of the aspects of truth. In fact, the series does acknowledge that there is some REAL power in Christianity, since when you obtain the Bible I was talking about earlier, it allows you to shoot fire. I'd also like to point out, that in the Bible, the Earth is flooded by God because there is too much evil in the world, and then, (slight spoiler coming) in The Wind Waker the Earth is flooded in order to destroy Ganondorf and his evil influence.
But that's all I have to say really. I do quite like to find small references in things and then to stretch them out in order to come to interesting conclusions about fictional worlds! A pointless exercise, some may say, but for me, this kind of thing is part of the fun of enjoying fiction.