the question of religion also exists. the original norse settlements followed traditional norse religious practices, descended from indo-european belief systems. christianity is a primarily semitic religion, although the sky god in judaism is...it's weird. semitic religions are not supposed to have dominant sky gods. that's an aryan religious characteristic. yahweh is oddly like zeus, or, more relevantly, the iranian equivalents. much of the symbolism in judaism seems to have been lifted from the religion of zoroastrianism during the reign of cyrus. this curious similarity between semitic christianity and the sky gods of european indigenous culture may have been a factor in the norse substituting yahweh for odin, in the end, as that kind of identification of local and foreign gods was common. the english word for german, for example, comes from the roman identification of odin with hermes. the french called it allemagne after a specific tribe, but the english called them "the worshipers of hermes". the germans called themselves deutsche, which in english only really exists as the word "dutch". the french celts would worship greek gods. and etc. it's not that weird for the norse to have combined the religions and, certainly, northern european christianity is deeply syncretic, and has major contributions from the indigenous germanic religions.
the fact that greenland was settled by people that worshipped odin at almost exactly the same time that norway was undergoing forced christianization from the top down suggests that some number of people that did not want to convert must have fled, and there is a written record of this happening in iceland, which saw a population spike by norse pagans after the violent introduction of christianity in the north, which was a long and violent process that had initially started under the rule of charlemagne in northwestern europe. the fact that william the conqueror was actually sent to england by the pope to overthrow the semi-pagan saxon kings is not widely acknowledged or talked about by english historians, but it is certainly true. the norman invasion of england was actually somewhat of a crusade against the saxons, who had been wiped out on the continent by charlemagne centuries earlier.
historians tend to argue that it doesn't make sense to think that the vikings would have abandoned greenland for north america because it would have cut them off from norway, but i think that misunderstands the context. i can think of two good reasons why the greenlanders may have not wanted norway to find them:
(1) the king wanted his taxes, and kings can get pushy about demanding taxes. it is entirely plausible that the settlers wanted to seek a way to avoid paying taxes back to norway, by making themselves hard to find.
(2) the king was sending christians to greenland and building churches and expecting the people to convert. i don't have any evidence one way or the other, but it's reasonable to expect that a large number of these settlers would have opposed this and sought to flee from it.
(3) another issue is the plague in europe, which happened at about the same time as the greenlanders disappeared. one way to avoid the plague ridden norwegians would have been to get up and disappear.
the fact that the greenlanders disappear at about the same time as the plague is tied into the fact that the norwegian capital, bergen, was essentially destroyed by the disease. the norwegians just didn't have time for greenland. the settlers might have taken the opening as an escape mechanism.
while the norse had a name for baffin island and for labrador, the official position is that there's no evidence of viking settlement in hudson bay. i would actually consider it extremely unlikely that any northern seafaring civilization could go to baffin island and not go to hudson's bay. that stretches credulity. but nobody's found it yet.
i strongly believe it's there and that archaeologists will eventually find settlements along the coast, dated to the years c. 1200-1600.
so, what happened after that? why didn't europeans find them during colonization?
there's some possibility that they actually did.
dna tests on groups in the region, like crees, suggest they're overwhelmingly r1*, meaning they descend from steppe warriors that invaded europe in the neolithic. there have been some awkward attempts to suggest there were european migrants to north america around that period, but they aren't taken seriously. it's generally accepted that it's a result of smallpox followed by colonialism, and that the reality is that the indigenous population was taken over by settlers from the inside. but the historical evidence we have for this doesn't suggest that is likely. it's a "no other option" hypothesis that doesn't sit right.
the other possibility is that the high r1* component in cree populations is due to viking admixture.
and, for all we know, they might have been eaten by polar bears when they tried to move south, into regions where there are more bears.
some settlements need to be found to prove this and i think they're there, but they have eluded archaeologists, who are also not looking very hard. i think they ought to be, because i think they're there, and they mostly left to evade paying taxes to a distant king with a weird new religion and a strange, frightening disease.