The most likely scenario is that actual Vinlanders would have very few syncretic beliefs because they would drastically outnumber the Beothuk within a generation or so and the relations between the Beothuk and Norse were very poor and don't have reason to get much better (unlike early English-Native or French-Native relations). Since Newfoundland is an island, the island would be remarkably pure Norse for a long time. I'd say the same goes for Markland--Norse and Indian would live in mostly separate worlds that rarely come together.
The area things would get odd is the fact that not every Norseman will stick around in the settlements on Vinland or Markland. These are the people who would really influence the natives because they would intermarry into indigenous tribes and would likely be receptive to missionaries. They would transmit concepts like pastoralism, Norse-style agriculture, and technologies like metalworking and Norse-style looms, which is to say the least revolutionary since their tribe would have a nigh-endless supply of trade goods to give to other tribes. Some might marry back into Norse culture, others would assimilate into native culture and leave some trace of Christianity. There were many native prophets who were baptised by missionaries and traveled around to other villages spreading their own version of Christianity, and only rarely did this have much to do with Christianity (usually baptism was a favourite ritual). I think tribes regularly in contact with the Norse would be a little more orthodox in their faith than that!
Now in Algonquian and Iroquoian culture, clans all had certain origins and responsibilities, so I could see folk Catholicism fitting in nicely with existing secret societies like the Midewiwin (and their equivalents). Metis people and those closely associated with them would form their own clan group. My guess is that due to the obvious power these Metis people would come to command due to their knowledge and connections, they'd come to dominate their tribes and ensure all leading members of society had at least some affiliation with the Church (but may well be free to practice their own religion in peace).
I 100% believe you'd have a conflict between secular and spiritual authority in this scenario, since Vinland will have at least one bishop nominally subject to the Archbishop in Nidaros. If we assume that like in Iceland, the Vinlandic church is forced to reform the insanely corrupt practices it no doubt would have had during the mid-late 13th century, by this era the bishop will want to keep things like that since that means he gains some say in who gets to be a priest. Maybe he's corrupt and lets the Metis people ordain unlearned men as priests who are free to marry and do whatever they feel (as in Iceland). Or maybe he demands men be educated and keep to celibacy, which since the only centers of education would be in Vinland, would ensure these men are sent there and learn more orthodox Christianity.
In terms of specific beliefs, obviously very little from Norse paganism since that was pretty much dead by 1200 in the Norse world. But from Amerindian beliefs, probably identification of the various spiritual beings and demigods with saints and demons. Belief in weaker spirits and the need to please them would persist, as they did in Scandinavia. Something like a wendigo would become a man possessed by demons.
BTW it's a little ASB to have Norse America be "cut off" since even Greenland wasn't cut off during the Little Ice Age and you don't need to sail that far north to sail between Newfoundland and Scandinavia. John Cabot didn't have . The reason sailing to Greenland declined was because Norway was absolutely depopulated after the Black Death and Denmark made for poor colonial rulers of medieval Greenland.