Ossetian here. What etan-tan wrote here is mostly true, but I want to add a little info about it.

Assianism is an attempt to create an organized religion based on what I call Ossetian traditional beliefs. I would ask you not to combine these two entities however, because Assianism is based on a lot of unscientific conclusions and a new age philosophy and weird attempts to form a philosophy based on values depicted in the Nart saga. The term Assianism itself comes from books of Daurbek Makeev, one of the authors of that neo-pagan movement. They are called Watsdin (Уацдин) here. Also claims about it being practiced in Ukraine seems quite weird, I don't understand where the author take it from. In fact, this article looks like it was written by someone from Eurasianists movement.

I also have read an article of Richard Foltz you mentioned. If you would look at it you would see that he points out the difference between the two and accepts that all these claims of continuity to the times of Scythians are unscientific. I'm not even going to mention that to call Ossetian religion a Scythian paganism would be a total misconception, since it's derived from Alan mythology, and those were two different people, even though of the same origins. And we know that even in related tribes their religious beliefs may vary a lot. The only continuity this religion could have is to Ossetian believes of the 19th century, yet, as I already mentioned, they are influenced more by modern philosophy.

Now, to talk about what Ossetian folk religion is. It is a syncretism of Alan paganism and Christian influences derived from the times of medieval Alania and it's attempts of Christianisation. In history we know a lot of examples of how people were mixing symbolism of Christian saints with their pre-Christian gods and how these saints were gaining different Pagan powers like being patrons of the weather and so on. This is exactly what happened with Alan religion at this period. Most academic scholars agree that monotheism which is present in Ossetian mythology, where you have only one being which has the status of God - Xwycaw, which is Ossetian name for God - is a concept derived from Christianity back in 10th century. Other deities, which all formerly had status of Gods, were "lowered" in their rank (they're basically a patron spirits called dzuars (дзуæрттæ) or dawags (дæуджытæ, this word is a part of common formula зæдтæ æмæ дæуджытæ - zads and dawags, though in this case you usually use a word бардуаг (literally patron-deity) and not дæуæг, which is usually understood as a more lower ranked divine entity) and also all got Christian names - like Wacilla, a deity of crops, thunder, lightings and rains, whose name consists of two parts Wac meaning saint, and Illa referring to Saint Ilya of Othodox tradition. Oh, and it's also important to note that Christianity influenced Ossetian holidays as well, for example Ossetians were celebrating Christmas (Cyppurs, being celebrated one week before the New Year, on December 26th) and Easter (Kwadzæn), even though in folk beliefs they lost their connection to Christ's name and had their own meaning. However, most academic scholars agree that they were influenced by Christian tradition.

Historic background of how it was preserved in this particular form is what you actually mentioned in your question. Alan eparchy of Constantinople patriarchy (yes, Alan Christianity was not that much connected to Georgians, it was introduced as part of alliances with Byzantium) was destroyed during invasions of nomads, though I must correct you that it was not destroyed by Mongols, but rather by Tamerlan who massacred all Alan settlements and drove them into the mountains where their religious tradition lost all connections with Christianity and remained in it's half-transformed form. European travellers who visited Alania prior to that were all pointing out that though Alans considered themselves Christians and knew the names of God and Christ, they were also worshipping their old deities and almost were not aware about Christian theology or philosophy.

We also know that pre-Christian believes of Alans were quite similar to Scythian ones. Roman sources claim that their main deity was a war god, to whom they were building altars in form of a sword which was put in the ground, and we have evidences that they also had a Seven-God pantheon, same as Scythians. We even have a supposed name of that pantheon. According to Abayev, one of the former names of Theodosia in Crimea was Ardavda, and it can be translated as "Seven Gods", and it may have been a name of their pantheon. So this gives more credit to a theory of a large Christian influence on Ossetian tradition, and that it is indeed a syncretism of two religions.

What you said about failed efforts of Russians to Christianise Ossetians in 19th century is almost true, since no one in Ossetia abandoned their old traditions, which contradicts to teachings of the Church. Majority of Ossetians who call themselves Christians still worship God and зæдтæ æмæ дæуджытæ the same way their ancestors did, because continuation of these traditions is considered a very important part of our national identity. And not only Christians, but also Ossetian Muslims do that. Their Islamic faith mostly consists in celebrating Muslim holidays, which they do in ADDITION to traditional Ossetian ones. Also, Ossetians hate being called Pagans, they believe that Paganism only refers to non-monotheistic religions, which is not the case with Ossetian one, and that Ossetian religion doesn't contradict any of postulates of Christian monotheism, no matter what priests would say.

What makes Assianism unscientific is that it denies all of the facts of Christian influences on Ossetian religion and instead of trying to understand it's real origins and influences they would make up a New Age-type philosophy to back up their claims. They would claim that Wacilla is not a Christian name, that he was worshipped by Scythians as well, and that all the facts of existence of Seven-Gods pantheon in Scythian and Alan mythologies are merely result of Greeks and Romans not being able to understand the meaning of Scythian rituals, and that Scythians were monotheists as well. They would claim that all academic scholars who were researching Ossetian history and traditions were bribed by missionaries and that they acted to destroy Ossetian religion. In fact, they're quite a weird guys who believe in conspiracy theories a lot.

Recently they were part of a scandal around excavations in the area of the Nuzal church. Nuzal church is a medieval Christian place which is believed to be a burial place of Os-Bagatar, known as Baqatar Ahasarfakiani in Georgian chronicles, a mythological founding father of Ossetian people and a historic figure - supposed last king of Alania (he was refered to as son of the king in Georgian chronicle) who was involved in failed attempt of conquest of Gori, city in Georgia, and re-establishing of Alan realm there after Alania in North Caucasus was destroyed by Mongols. Assianists declared that what archeologists were doing there was a desecration of traditional holy sites and that all evidences of this place being a Christian one were faked by them.