And Youma Boxsy is King of Kings! He said so, so it must be true.
Naru is shown praying in episode 87 as Usagi runs off. They don't say who to, though, and I'm not sure if that type of hand clasped maneuver is common to other religions. She approaches the christian priest in episode 26 who became Youma Boxsy, but that could just be because it was the first person she saw in the first graveyard she saw while she was out that day, in light of the grieving she was going through.
The Chronos thing is particularly interesting, because it's part of the invocation Chibi-Usa uses when activating the Key of Space-Time. That suggests Chronos is literally real to some extent in the Sailor Moon setting, and is involved in the time travel technology of Silver Millennium/Crystal Tokyo somehow... then again, Serenity (/Selene) and Endymion are also from Greek Mythology, though a lot of liberties are taken with regards to their societies and personal capabilities and such, so Sailor Moon's Chronos is probably a bit different from Greek Mythology's Chronos, too.
There's also Sailor Lethe in the manga. (Not to mention all these planet names are also Roman god names.)
And another thing many people miss if they aren't familiar with buddhism is that the Shitennou are mythological buddhist figures, the Four Heavenly Kings associated with the wind and the four cardinal directions. That's the basis for the territories they occupy in the Manga- Nephrite is West, Zoisite is North, Jadeite is East, Kunzite is South. The mineral association, though, is a Sailor Moon invention as far as I know, and obviously the personalities and specialties are up for debate. (Not like the God Jupiter is really known for shooting flowers, or the Moon or Selene associated with clumsiness, etc.) On top of that, Nephrite references a lot of astrological lore in the anime, so that's a whole other set of religious associations.
Anyway, these previous interpretations of Rei's attitudes sound about right to me (though I still haven't seen the live action series yet). Shinto and Buddhism are, as far as I understand it, very often practiced in tandem because the bulk of their content addresses different concerns (with Shinto focusing more on rituals for cleanliness and maintaining crops and practical orderly stuff like that, while Buddhism focuses more on deeper existential questions and ethical abstractions. At least, as far as I know, I'm no expert either).
But in particular, monotheism is not widely practiced in Japan, so from what I can tell Christianity gets casually lumped into life to various extents (depending on personal interest and social factors and stuff), but not to the exclusion of other practices, contrasted with the United States where exclusive monotheism is much more common.
Christian symbols are also used very casually as a stylish or almost slightly magical thing in japan, particularly crosses. Naru Narusegawa in Love Hina routinely wears a cross necklace (at least in the manga), but there are no other signs of her practicing that religion and she instead attends various shinto rituals during the story (to say nothing of the random weird magic in that setting). And then you've got things where it's playing off it more deliberately, but still treating it in a bit of a fantastical way, like Castlevania, where crosses are a magic weapon good against the undead and most often act like boomerangs.
So basically, Rei probably puts more personal investment into Shinto than Christianity, but she can still attend a Christian school due to various cultural reasons, and be friendly with it without that really violating her own religious convictions. But that attitude might or might not be fully appreciated by the people running the school, though they are also probably pretty used to that sort of thing. I assume there's some sort of longstanding set of rules about how people working for such institutions even approach bringing up the monotheism issue, and that it amounts to 'very carefully'.