Ancient Egypt was a polytheist culture - although monotheism was briefly instituted by Akhnaton, only to be forcefully rejected after his death - and so "religion" was a matter of common beliefs and practices, rather than something hingeing on one deity. Most notably, the Egyptians believed that the Pharaoh was a divine emissary (the word means "house", as in, the body of the leader of Egypt housed the gods) and that for the soul to survive after death, it was necessary to keep the dead body intact. Opinions of "intact" differ; I wouldn't consider intact a body whose brains have been removed through the nose, neither do I envy the people whose job it was to remove the entrails, pickle them separately and reinsert them in a nicely wrapped package before the whole corpse was bandaged in linen and put in its final resting place. But it was worth the trouble to the ancient Egyptians, who painted murals of the deceased's soul, in the form of a bird, alighting on the body that sustained it. The body that was the house of the gods deserved special attention: it was not only embalmed, but provided with the characteristic triangle-based tomb to whose shape and proportions mysterious powers are still ascribed, and which must have cost a heck of a lot to construct. Filled with precious artifacts, these tombs, the pyramids, held a strong attraction for grave robbers, myths of mummy curses notwithstanding; though what killed the odd archaeologist was probably not the mummy's vengeful spirit, but the sometimes very nasty bacteria surviving inside the not-so-sterilized corpse, ready to pounce as soon as the bandages were removed.

It's been a long time since the beliefs of the ancient Egyptians were practiced on a large scale, so what remains is the popular image of the vengeful mummy. In episode 3, a mummy plucks planes from the sky in one of Galactor's overblown schemes ("We need the invention of someone who may be on a plane, let's smash all the aeroplanes we can find") while in episode 69, the team get their own back by donning mummy disguises and scaring the living daylights out of a bunch of Galactors.

Near an airport, a mummy appears, assuming the usual "I'm a monster about to grab you" pose. (See the middle pic to get an idea of its size.)

Buddhist

"Buddha" was no more the real name of the historical figure than "Mahatma" was the real name of Gandhi; it means "awakened" and was the title awarded to the inventor of enlightenment. As far as I know, his real name was Siddharta Gautama (his wife's name was Yashodhara, for anyone interested), and he was a prince in ancient India who led a cosseted and carefree life, until the day he saw his first corpse. Inquiring what it was, and so getting his first taste of mortality, he set off on a personal spiritual quest to discover the meaning of this phenomenon called "life" before it slipped through his fingers, and in the course of much praying and meditation and trying this & that, one day achieved enlightenment while sitting under a bodhi tree.

So far, the probable historical background. Slipping into myth, Buddha might have kept his discovery to himself, but Brahma, principal god of the Indian pantheon, argued that there were people who needed just a slight push to achieve the same, and persuaded him to go public. And so, today, Buddhism is common in the extreme East, having made its way into China, Japan, Singapore, Birma, and most notably Tibet, where it became an amalgam of god-worship and religious practices that probably have little to do with the original.

Christian

It all started with a tribe living in Mesopotamia, the present-day Iraq. (Some still live there, they're incorrectly called "marsh Arabs".) Due to religious differences with their neighbours, the Sumerians, they left for a "promised land", picking up snippets of lore from the countries they passed through and finally settling in the Middle East where, in due time, they fell under Roman control. In that age of priests and prophets, there was a young troublemaker who thought he knew better than the religious Establishment, and was getting a fair following. The priesthood requested the Roman authorities to put him to death, and with some reluctance their wish was granted. This had an adverse effect; the new belief spread like wildfire and before long, the Romans found themselves having to take action against these Christians who refused to honour any god but their own, not even a late Roman emperor elevated to divinity.

It is probably through the Roman empire that Christianity spread into the far reaches of Western Europe, from where, in the era of colonization, it went on to conquer the Americas, thereby firmly planting the false idea that Christianity is something Western. It was certainly accepted more readily in Europe than in China and Japan, where missionaries had the inconsistencies of their beliefs pointed out to them, and generally got laughed in their faces. But the Japanese are nothing if not adaptable, and Judeo-Christian icons have found their way into manga, anime and games - sometimes in an unintentionally hilarious way.

Hinduist

Native American

The kachina belongs with the Hopis, whose name translates to "peaceful people", although their older name is "Anasazi" meaning "ancient enemy", given to them by their old neighbours, the Navajos, in remembrance of less peaceful times. It is either one of a number of spirits - Corn Maiden, Spider Woman and there may be a Buffalo in there somewhere, although the Hopis were not a buffalo-hunting tribe - or a dancer dressed like one of these in a religious ceremony, or a doll made to represent one of these. Kachinas (I think the proper plural is "kachinam") live in the hills and come down to visit mankind every year to help the crops grow; they are beneficent spirits, at least I can't recall a kachina bent on destruction. They have no neat catalogue of names, and their total number is unknown, probably because each village has its own local spirits.

The Hopis have an interesting set of prophecies about the end and rebirth of this world which seem to involve aliens, a fact which the writers of the X-Files seized on to protract their alien contact saga; and alien appearances are said to be sometimes heralded and accompanied by an immobile, obscuring cloud. However, Hopi prophecies don't mention a metal superbuffalo stepping out of said cloud with wings on its back.

Cripes, Arizona had an unexpected visitor. A ripped-off metal horn (snagged a rock during the rampage?) reveals the manifestation may not be so supernatural.

The human sacrifice

One religious practice which these days is considered both ancient and barbaric - and therefore perfect for exotic locations in old Hollywood films - is human sacrifice. Laid out on a stone slab, possibly tied down to ensure cooperation, the victim lies face-up, wide-eyed, as the high priest(ess) raises the sacrificial dagger, then plunges it into the victim's chest and rips out the heart, all this preferably at the first or dying rays of the sun, with a hypnotically chanting gathering of worshippers and possibly some musical accompaniment.

In practice, as some Celtic priestesses could have told, ripping out the heart isn't so easy; it may require the prior breaking and removal of obstructing ribs, during which procedure the patient was required to laugh in a show of bravery. (That'll be a short and final show, then.) In ancient Crete, the sacrifices were stabbed in the neck to bleed to death. In various locations around the Mediterranean, babies were burned. The fertility gods demanded that the first of the harvest be given to them: the first ears of corn, the first lambs and kids and, possibly in the spirit of equality for all living things, the firstborn infants - all these were popped into the holy furnace. Annual sacrifice of a young male (the "king") to ensure a good crop the next year was a practice in hazy distant times which led to the Adonis myth and the traditional making of corn dollies, decoratively woven wheat stalks said to house the spirit of the Corn King through the winter; how this sacrifice was carried out, I don't know. There was a time in history when human sacrifice was simply very much en vogue, and different forms of worship entailed different methods. When it comes to doing a lot of carving, the Aztecs had the showiest rituals, beheading and gutting the sacrifice and hanging the bowels out on a rack.

Why exactly this ninja-sacrificing ceremony strikes me as fake Aztec, I don't know; it may be Jinpei's mask. Why this ceremony was held at the new mecha's inauguration at all, I can't tell - maybe they'd run out of champagne bottles.