All of the references are either astronomical, biblical, or otherwise based in Judao–Christian tradition.
The twelve apostles, the ten commandments and the four gospel makers should need no explanation. Of the other sets, some are more obscure than others.
"The eleven that went to heaven" refers to the eleven apostles other than Judas Iscariot. The "nine bright shiners" is obscure; Wikipedia suggests that it may refer to the Sun, the Moon and the five planets known since ancient times, along with "the sphere of the fixed stars" and the Empyrean Heaven – the highest place in heaven in Aristotelian philosophy, or in Christian literature, the dwelling place of God.
The April rainers are the stars of the Hyades – the nearest open cluster to Earth, and as such one of the best studied by astronomers. The Hyades are known as the April rainers because they are associated with the showers in April, when they rise with the Sun.
I believe I have heard this line sung as "the eight bold rainers", but I may well have misheard it! Either way, it would appear to be a corruption of "the April rainers".
The "seven stars in the sky" is probably a reference to the Pleiades, also known as the Seven Sisters – another of the star clusters nearest to Earth. Wikipedia lists a couple of other possibilities, including the seven stars of what we know in Great Britain as The Plough (the Big Dipper to North Americans).
The "six proud walkers" may be a corruption of 'six proud waters' – the six jars of water that Jesus turned into wine in his first miracle, at the wedding feast at Cana.
The"symbols at your door" may be a reference to the practice, common in the late Middle Ages and the Early Modern period, of putting a pentagram at the door of a house to ward off witches and evil spirits. Another possibility is that the five symbols are those displayed above the doorways of houses that would shelter Catholic priests; this would date this line, at least, to no earlier than the Reformation. But the theory that Wikipedia gives top billing to, associates the symbols with the mezuzah – a piece of parchment, contained in a decorative case and inscribed with specific Hebrew verses from the Torah, which consist of a Jewish prayer. A mezuzah is affixed to the doorpost of Jewish homes to fulfill a Biblical commandment to "write the words of God on the gates and doorposts of your house".
Cecil Sharp recorded four variants to "the symbols at your door", which he was unable to explain: "the boys upon the pole", "the thimble over the ball", "the plum boys at the bowl" and "the plum boys in the brow".
Wikipedia suggests six possible explanations for "the rivals". The first possibility is a corruption of "riders", "arrivals", or "wisers", in reference to the three Wise Men. The second refers to the Holy Trinity (the "rivalry", apparently, is concerned with early Christian debates about the nature of the Trinity). The third trio is the apostles Peter, James and John, among whom (according to St. Luke's gospel) "there was a strife ... which of them should be accounted the greatest". The fourth (according to a Lutheran pastor in Sacramento) are Shadrach, Meshach, and Abednego, who resisted burning in the fiery furnace and were "rivals" to the Babylonians. You may feel that the suggestions are getting more and more esoteric, but the fifth is almost laughable (IMHO), despite the assonance. There is a group of mountains in Snowdonia, known in Welsh as Yr Eifl – "the forks". The Welsh name is pronounced 'err eye–vl'; it rhymes with the English word 'rival', and it's easy to see how the suggestion arose.
Wikipedia's sixth suggestion is that "the rivals" are Hera, Athena, and Aphrodite, the three goddesses in Classical mythology between whom Paris, a Trojan mortal, was asked by Zeus to choose the fairest (who would receive the golden apple from the Garden of the Hesperides, as suggested by Eris, the goddess of discord). For the record, Paris chose Aphrodite. Wikipedia fails to explain however how a story from Classical mythology made its way into an ancient English folk song.
"The lily–white boys" (clothéd all in green–O) are probably Jesus Christ and John the Baptist, both of whom were born without original sin. Again, Wikipedia suggests several alternative explanations, the most convincing of which (IMHO – suggested by Baring–Gould and cited by Sharp) is that it's a reference to the constellation Gemini, the Twins – the northernmost constellation in the zodiac, therefore high in the winter sky in the northern hemisphere and sometimes clothed in green by the Aurora Borealis.
The One who is One and (stands) all alone, is almost certainly God – although I would suggest that if the theory about the Holy Trinity being "the rivals" is anywhere near the truth, the folk tradition is getting its metaphors somewhat mixed up.
© Haydn Thompson 2021