Would Utena choose Christianity?  Hmm...

Utena is like almost every other member of the cast in that she wants to believe in "something eternal."  That need for the eternal is a core theme of the show, and for Utena eternity manifests itself as her memory of Dios.  Utena's other core need, which is closely related to the first, is the need to feel like she personally has the power to help people who are suffering.  This is the need that got her out of her coffin after the death of her parents.  She believes that a person can suffer and suffer and go on suffering; she doesn't believe that there's a cosmic force out there that will step in and save someone if no person takes the task into their own hands.  Utena takes to heart her principles -- never lose your strength or nobility -- because these principles connect her to eternity and enable her to protect others.

I don't think Utena is of a philosophical enough bent to identify as a humanist, but I think that's the "religion" that her beliefs and actions actually express.  Does she believe in the divine?  Maybe and maybe not; she doesn't talk about God in the show except very superficially.  I don't think she spares much of a thought for God or gods.  She certainly doesn't go around expecting divine intervention -- even though, ironically, the divine does in fact intervene on her behalf regularly!  What matters to her are human actions, especially her own.  Is she being her authentic self?  Is she doing her best for those around her, as best she knows how?  Then she's fine.  That's humanism in a nutshell.

That's not to say she wouldn't feel some resonance with Christ!  Christ is both a savior and a sufferer, and the prince archetype Utena aspires to (as well as the witch archetype Anthy gets stuck with) explores and subverts both those roles.  But I think she's unlikely to go "therefore, Christ was the son of God and died for our sins."  That doesn't fit with her understanding of the world as a place where eternal suffering is conceivable.  Instead, she's more likely to go "therefore, I want to be like Christ."  That doesn't make her a Christian; it just means she shares some of Christianity's values.

My two cents.

I've always assumed Anthy was probably Hindu since she wears a bindi, though I'm not really sure if it's only a Hindu thing or if it's also a part of other traditions in South Asia. & she keeps wearing it when she leaves Ohtori, which marks it as part of her individuality rather than part of the Rose Bride getup. I also feel she'd identify strongly with Sophia in Christian and Gnostic tradition, though. Well, if you assume the songs on the Rose Egg Sophia album were chosen because they are relevant to the show, somebody sure does.
I feel very strongly that Touga is Gnostic. I mean, he quotes Hermanne Hesse's Demian directly in most episodes (in the egg speech) and listens to it on repeat when he's upset; it's clearly very important to him. I think his religious beliefs would very much revolve around Abraxas. He definitely would have gone on to do more research and found Jung's Seven Sermons to the Dead, like I did, though he couldn't have read the whole Liber Novus since it wasn't published until 2009 (...unless Akio got his hands on a copy and let Touga read it, which actually isn't implausible). I think he'd also read Niesche and Novalis because they're praised highly in Demian. Also, maybe, the Greek magical Papyri, because they mention Abraxas. As for actual Gnostic texts, there are a lot, but he'd read whatever he could find and connect with some of them more than others, as anyone would.
Imo Akio is an alchemist. I know that's not actually a religion, but that's my headcanon in terms of Akio and religion. If you have to put it in religious terms, a hermeticist... only, it's not like he'd worship Hermes Trismegedus or however it's spelled? Rather, the opposite, wanting power over this god. Naturally, I've got very specific reasons for this, and it has to do with Virtual Star Embryology! That line about the egg hatching into a philosophical child (or child of philosophy as it's more often translated)--well, that's an alchemy thing. The philosopher's stone was also called the philosophical egg and philosophical child, and also sometimes the bird of Hermes. It's the same metaphor as in the speech Touga keeps quoting, just a different context... and in this one, it's sinister. The western alchemists (the ones I know the most about right now) were about creating new life and then controlling it. The methods for "taming" the Bird of Hermes could be really gruesome. I think it's very poetic... all these students are striving to break out of their shells and be free... but the way they go about it is entirely controlled by Akio who is manipulating them all for his own ends.
I feel like Saionji would be very dedicated to whatever tradition he was raised in, but we don't have too many hints about what that is.
This is probably the most weirdly specific thing anyone will have to say, but I think Tsuwabuki has been reading Charles Fourier and taking it way too seriously. His duel song--the word that gets translated as 'algebra'--it's not algebra. It's an understandable mistranslation because it's actually the katakana for Archibras, which isn't a real word. It's French and not something you'd find in a French dictionary. This Fourier guy thought that the human beings of the future would develop a tail with a hand and an eye on the end of it. I think Tsuwabuki, in his attempts to be "grown-up", has been reading books he doesn't understand which he thinks is because they're so advanced, but actually they are ridiculous. He'd be super insecure about not understanding it, too, probably. This was actually an idea my friend Toby brought up to me when I found Archibras in the song title and told him about it.

While I don't think she'd make a good Christian, Anthy - particularly movie Anthy - buys into the very gnostic Christian cosmogony of a desperate false god and all that, re her brother and her situation, her wholesale acceptance of her deserved eternal punishment and collusive behavior due to fatal original sin... she'd be a "weird Catholic mystic" to steal from Kerouac. If she isn't already.

Juri would be god of the atheists. Even the flying spaghetti monster would get her hackles up.

Miki... I can easily see Miki bowled over by the first proselytizers to knock on his door.

Saio would be an old school Japanese animist, but at like a child's level forever.

Touga... worst Jesuit priest ever? But with a big ol' crucifix.

And, Wakaba'd be a fair-weather buddhist.