Okay, let me see if I can summarize all the input.
Sweden already had a Christian minority since the 830s, resulting from the efforts of Ansgar, the Apostle of the North. Through the 9th century, Västergötland (West Gothland) became increasingly Christian. While the rest of Sweden probably had few Christians, if any at all. Olof Skötkonung, King of Sweden (reigned 995-1022) became the first true Christian King. Baptized by a missionary called Sigfrid. But unlike his counterpart in Norway, Olof was in no position to violently convert his subjects. He helped set a new Bishopric at Skara, but conversions were peaceful, voluntary and few in numbers.
Yes, Olof Skötkonung was the first “true” Christian king of Sweden (I was under the impression that his father Eric Segersäll converted late in his life, but considering that it is well known that he would worship Odin before his battles, I'm willing to grant King Olof the “true” status), and that after that Asatro and Christianity managed to live somewhat peacefully side by side for some time. At the end of the 11th century though, things start getting a bit thougher for the Heathens, when Inge/Ingi the Elder becomes king. As Hervarar Saga tells us:
“Steinkel had a son called Ingi, who became King of Sweden after Haakon. Ingi was King of Sweden for a long time, and was popular and a good Christian. He tried to put an end to heathen sacrifices in Sweden and commanded all the people to accept Christianity; yet the Swedes held to their ancient faith. King Ingi married a woman called Mær who had a brother called Svein. King Ingi liked Svein better than any other man, and Svein became thereby the greatest man in Sweden. The Swedes considered that King Ingi was violating the ancient law of the land when he took exception to many things which Steinkel his father had permitted, and at an assembly held between the Swedes and King Ingi, they offered him two alternatives, either to follow the old order, or else to abdicate. Then King Ingi spoke up and said that he would not abandon the true faith; whereupon the Swedes raised a shout and pelted him with stones, and drove him from the assembly. [...] They drove King Ingi away; and he went into Vestergötland. Svein the Sacrificer was King of Sweden for three years.”
(All this can be found in the wikipedia entry on Inge, by the way). Inge is then exiled for three winters before returning to reclaim the throne:
“King Ingi set off with his retinue and some of his followers, thought it was but as small force. He then rode eastwards by Småland and into Östergötland and then into Sweden. He rode both day and night, and came upon Svein suddenly in the early morning. They caught him in his house and set it on fire and burned the band of men who were within. There was a baron called Thjof who was burnt inside. He had been previously in the retinue of Svein the Sacrificer. Svein himself left the house, but was slain immediately. Thus Ingi once more received the Kingdom of Sweden; and he reestablished Christianity and ruled the Kingdom till the end of his life, when he died in his bed.”
Inge goes on to burn the old Temple at Uppsala, and erects Uppsala Cathedral at its old spot to assert Christianity's supremacy. After that, most of the nobility embraces Christianity, and even though it will still take centuries for the ancient folk beliefs to die out, most of the population rapidly becomes Christian.
The discovery of Vinland coincides well with the reign of Olaf the 1st and his persecution of pagans, if he has a change of heart and decides to exile the pagans to Vinland instead of torturing and killing those who refuse to convert Vinland could soon have a settler population of over 10 thousand or more. He doesn't necessarily need to be hugged by a Carebear he could reason that too much terror would lead to insincere conversions. A viable Vinland colony would mean that Iceland and Greenland would not need to rely on Norway for timber etc. This POD also adds a nice pagan flavor to Vinland making them genuine vikings.
I like this scenario a lot, though as Henriksson mentioned before, there is still the question of whether such a trip could actually be viable for many people in any larger exodus-style emigration of pagans. However, you do point out something very interesting here, namely that a viable Vinland colony would mean that Iceland and Greenland would not need to rely on Norway for timber etc. This is very interesting since as it was Iceland's dependence on Norwegian resources that allowed the Norwegian Crown to eventually reassert their rule on Iceland and the supremacy of Christianity:
"He [King Olaf] refused Icelandic seafarers access to Norwegian ports and took as hostages several Icelanders then dwelling in Norway. This cut off all trade between Iceland and its main trading partner. Some of the hostages taken by King Olaf were the sons of prominent Icelandic chieftains, whom he threatened to kill unless the Icelanders accepted Christianity."
The response was somewhat predictable. The adherents of the two rival religions heatedly argued about the proper way to address the situation. But pragmatism won the day. In 1000, Thorgeir Thorkelsson, law speaker of the Althing , decided in favor of converting Iceland to Christianity. He was himself a pagan priest but made a show of his conversion to the new faith. His initial terms included that the pagans were still allowed to privately practice their religion at home. The church banned this practice a few years following the official conversion.
From history it is known that Leif Ericson discovered Vinland about a year or so after Thorgeir's conversion, so it seems quite hard to keep paganism alive and thriving under such conditions. But how about this, then? As Dan1988 suggested, what if Vinland is explored earlier, say by Eric the Red (a pagan), who is curious about Bjarni Herjólfsson's account of the land sometime in the mid-980s, and this is combined with the Thule moving further south rather than east?
Thus, when Norway starts to exercise their pressure on Iceland, it is already known that there exists a pagan-friendly settlement in Vinland, where there most certainly can be found timber. This gives the Althing the courage to stand up for their old beliefs and Thorgeir consequentially does not convert. In this environment, in which Eric has organized a permanent settlement on Vinland, Leif does not convert to Christianity either. After some limited struggle, the Norwegian Crown is forced to accept the sovereignty of Iceland as far as religious matters are concerned, as they are uninterested in wasting too much resources on a religious war against an island several miles away. With a continued pagan Iceland, it is then reasonable that when the rest of Scandinavia is Christianized during the 11th century, many pagans emigrate to Iceland, from which they continue to Vinland via Greenland.
With a couple of stops on the journey in pagan-friendly places, a minor exodus becomes somewhat more viable. Thus, it is possible to have more Scandinavian pagans emigrate to North America forming a large settlement in Vinland. Add in the discovery of the multitude of fish in the water and a very scarcely populated area and we can allow for the Norse population to expand rapidly.
Eventually trade will resume between Iceland and Norway, thus allowing for trading routes between the Old and the New Worlds.
Would this make it plausible?
