This is one of those "not even wrong" propositions, so it's hard to know where to start with how wrong it is. First, let's just face it that when the people touting this line say "white," they mean Europeans, although with a few exceptions we can touch on later. So, let's try and break this down into 3 parts:

1. Confusion over myths and folklore

2. Post Conquest ergo propter White Gods

3. Bad anthropology

1. Confusion over myths and folklore

In this case, what we have is often a long chain of oral traditions, myths, legends, religious practices, and folktales which then get reinterpreted by people outside that tradition into a form the outside understands. One example of this is the idea of pale "moon-eyed" people in the Southeast of North America, which James Mooney ascribes to a group in the area with a high incidence of albinism, but which our own /u/reedstilt thinks is more likely an etic interpretation of supernatural beings. Regardless, the idea gets jumped on by some people as "evidence" of white (i.e., European or European-descended) people where no white people should be... and therefore THE HISTORY YOU HAVE BEEN TAUGHT IS A LIE!

OK, maybe not, but these claims always come with a strong whiff of anti-establishment, second-option bias smugness, if not outright conspiratorial thinking.

The moon-eyed folk being a bit thin on evidence, let's turn instead to South America, where the Inca had a god/culture hero often called Viracocha who was a "white man of great stature," at least according to 16th Century chronicler Pedro de Cieza in his Chronicle of Peru. De Cieza also writes that he was told some of the great old cities in the Andes, like Huari and Tiwanaku, were constructed by "bearded men on the island of Titicaca" and that an Inca ruler had done battle with these people on the island, who were "white people who had beards."

Of course, Juan de Betanzos' Narrative of the Inca, which was written at the same time, tells a different story. He instead writes that Viracocha was a "tall man dressed in a white garment." The difference is that while de Cieza was a Spaniard who only arrived to his works after the fall of the Inca state, de Betanzos' work is drawn from the history told to him by his wife, who was a Quecha and a member of the ruling dynasty of that state. The latter work is the more direct, emic account of Viracocha.

In Mesoamerica, there's often a confusion over some deities being called "White," but this does not refer to skin color. Mesoamericans associated certain colors with cardinal directions, such that Miller and Taube note, in The Gods and Symbols of Ancient Mexico and the Maya, that white was associated with North among the Maya, though this not standardized across the whole of Mesoamerican places or times. This colors/directions were symbolic of aspects of a deity, such that Markham and Markham in, *The Flayed God: The Mythology of Mesoamerica," recount a version of the creation myth where a pair of creator deities give birth to 4 different aspects of the god Tezcatlipoca: Xipe Totec-Camaxtli-Mixcoatl (red/East), Tezcatlipoca (black/North), Huitzilopochtli (blue/South), and Quetzalcoatl-Yohualli Ehecatl (white/West). A "White Quetzalcoatl," then, is merely a symbolic/artistic association, not an ethnicity.

2. Post Conquest ergo propter White Gods

There is a persistent myth that when Europeans (particularly the Spanish) arrived in the Americas the locals thought they were gods, specifically white gods who had been prophesied to return and conquer. This myth has had staying power in part it helps to "explain" how small numbers of Spaniards could easily conquer large and powerful states like the Aztecs and Inca. I put "explain" in scare quotes because the only thing it explains is that simple, incorrect, answers are often preferred to more complex explanations like these conquests weren't done by just a few Spanish, weren't easy, weren't complete, and are overall much more complicated and interesting than "White Gods, QED."

I'm not going to spend more time on this, instead linking you to two past posts about the Aztecs:

• Is there any truth to the commonly cited fact that the Aztecs believed the Spanish were gods?

• Did Moctezuma II really believe Cortes was 'an armor-clad God'?

3. Bad Anthropology

Let's start with beards, and the fact that Native American men, being Homo sapiens, can grow them. Body/facial hair may not be as profuse among Native Americans as among certain other groups, like Europeans, but it exists, though was often plucked as it grew in. Hernan Cortés himself describes the Aztec ruler Motecuhzoma Xocoyotl as having facial hair, saying "his scanty black beard was well-shaped and thin." Likewise our pal de Cieza makes a few mentions Andean men have facial hair, though thin. Because there is a stereotype that indigenous Americans are unable to grow facial hair, however, mentions of "bearded gods" gets re-interpreted as "white Europeans." This occurs even in cases, such as with depictions of Quetzalcoatl -- who, let us not forget is feathered serpent god -- where a ruff of feathers might be called a beard.

Next, "white" skin is relative and gradations of melanin exist even within the Americas. To cite de Cieza again, he specifically notes that Chachapoya women were "very white." De Cieza, like most of the early Spanish is the Americas, was from Southern Spain, so we also need to take into account that when he writes to other Spaniards that he sees people who are white "like ourselves," his comparison point is men from Andalucia and Extramadura who are spending a great deal of time out in the Sun.

Then there is the Solutrean Hypothesis. To put it succintly, this is a (completely discredited) notion that, during the last Ice Age, northern Europeans crossed over the North Atlantic to settle in North America, but were killed/outbred/assimilated by later migration across the Bering Land Bridge. The original basis for this was a seeming similarity between spear points in North America (Clovis) and Europe (Solutrean), despite 1) there being several thousand years between those archaeological styles in those regions and 2) people who study Clovis material saying they are, at best, evidence of parallel evolution of styles and, at worst, not at all similar. Later the proponents of the hypothesis tried to claim that the presence of haplogroup X, which is uncommon in East Asia but common in both Europe/West Asia and Northeast America, was evidence of a genetic connection. The particular subgroup of X in the Americas, however, was entirely separate from the Eurasian subgroups and actually supports the Bering migration.

You can read more about the Solutrean nonsense in past comments here and here.

This, of course, brings us to racism, which is the worst kind of anthropology. Early on, Europeans struggled to explain 1) how there were people in the Americas, despite this not being mentioned in the Bible, and 2) how these "primitive" people could build such monumental architecture found in Tiwanaku or Teotihuacan. You can read some of those contortions in this past comment. Later this paired with scientific racism which "proved" that Native Americans were incapable of civilization and therefore it must have been introduced by Hebrews, Romans, Celts, Egyptians, or anyone other than actual Americans. Ideas like the Solutrean Hypothesis actually feed into this and it has become quite popular with white Supremacists who glom onto these ideas to "prove" that white Europeans were the original inhabitants of the Americas... and therefore the numerous genocidal acts inflicted by Europeans on Americans is OK? The reasoning has never been clear to me, but the fact remains that white Supremacists are big into taking all the out-dated and debunked nonsense above and using it justify any number of twisted conclusions. So you many want to casually ask your friend if he's read Mein Kampf or perhaps has a double lightning bolt tattoo or an affinity with the numbers 14 and 88.

I should also point there's a fourth category of nonsense about this that we haven't covered, which is:

4. Aliens

Tsoukalos, von Daniken, and the rest love the White Gods because, well, you gotta get paid somehow.