I think there isn't religion in Equestria. Everything they believe is either scientific fact, or magical fact, or divine revelation (i.e. directly from Celestia herself). Celestia and Luna are the physical gods, as well as Discord.
I've considered this before, and I think there is religion in Equestria but they don't talk about it much. They occasionally use words with religious connotations (Rainbow Dash: "My prayers have been answered!" Applejack: "Heaven forbid that should happen." etc.). Also, the princesses aren't gods as evidenced by the fact that they aren't omnicient (Celestia mistakenly thought that Changeling Cadence was real), their subjects don't pray to them (they send her letters), and they're not omnipotent (extremely powerfu, yes, but Chrysalis did manage to beat Celestia in a direct confrontation).
The idea of an omniscient, omnipotent, and omnipresent One God is just one of many ideas, and there are more than one way to hypothesize the existence of gods.
Consider Greek mythology. The MLP universe is very very close to the Greek mythology universe, with Cerberus, Tartarus, Pegasus, and Unicorn (though technically, Unicorns are not found in Greek mythology, but rather in accounts of natural history, for Greek writers of natural history were convinced of the reality of the unicorn, which they located in India, a distant and fabulous realm for them.). It is natural to think that the MLP world is a polytheistic world, very different from the monotheistic Abrahamic religions. In such a world, the gods are not that powerful, can make mistakes, and can be defeated, even killed.
And there was the creation of new gods, the Apotheosis, i.e. Twilight's Coronation.
As for the religious connotations, I think they are lingual remnants from a dark time, a time when the mortals did not know the physical presence of Celestia and Luna, and resorted to imagined gods in the heavens.
And they do pray upon Celestia. Pinkie Pie: "Thank Celestia you are OK!" Applejack: "Thank Celestia!" Rainbow Dash: "In the name of Celestia, just sit here and do nothing!" Rarity, and later, Fluttershy: "As Celestia as my witness!"
I assume that you based your view on MLP on Christianity, though I cannot pinpoint the exact division. Maybe Liberal Christianity, since you like Christian Heavy Metal? I'm an atheist, majoring in physics and math.
My headcanon creation story is that, at first there was chaos (Ex nihilo chaos fit), then there was Discord, the physical embodiment of chaos (or as physicists call it, entropy), emerging from the primordial chaos. Then Discord felt bored and, just for fun, created ponies, griffons, goats, lions, etc to his own (partial) image (explaining why Discord looks like a collection of all of them). But then he realized that he could not keep the mortals alive without feeding them negentropy, so he created two sources of negentropy, the sun and the moon.
However, he did not realize that out of the sun and the moon, two powerful gods emerged, Celestia and Luna. They were the physical embodiment of the life cycle, with Celestia controlling the sun, the birth, the growth, and Luna controlling the moon, the death, the recycling of organic substance.
At first Discord thought they were not a threat. One day, due to a love potion (refer to Hearts and Hooves Day), a pony kingdom fell. The ponies, in a desperate cry for help, asked upon Discord. Discord thought "why not? It may be fun!" and became their political ruler. However, Discord was a troll at heart, and soon his oppressive rule proved too much. Ponies were dying in hoards, and this infuriated the Sisters. They wielded the Elements of Harmony (the crystallization of life, because harmony is the homeostasis) and imprisoned Discord.
I'm not sure that saying "Thank Celestia" and "As Celestia as my witness" are really equal to prayer. And, pertaining to the original question of whether or not there is/was religion in Equestria, your fourth paragraph seems to suggest that there was. I don't really wanna argue headcanon with anyone, though.