Norway had religious tolerance from 1000 to 1015; but Olaf Haraldsson went on to enforce Christianity by violence till 1028.
Thorgeir had OTL made concessions to heathens on Iceland in 1000; but those concessions were repealed in 1024.
If Thorgeir in 1000 made concessions to Christians but kept Iceland officially heathen, many of the Christians in Iceland would regard concessions as insufficient. As would many Christians outside Iceland. So, with Olaf Haraldsson interfering, things can get hot in Iceland around 1024.
Now, remember how few people were needed to settle Greenland. There were just 560 people who arrived on the invitation of Erik. The Eastern Settlement would support over 2000 souls. And yet Erik advised to split the settlement and send a part of people to Western Settlement, hundreds of km away.
Suppose that L´Anse Aux Meadows settlement survives and thrives. It is far to the south of Greenland, with warmer summers - they can grow grain there, and sell grain, timber, ships and iron to Greenland and Iceland. In OTL, Iceland and Greenland had to import these. The settlers did find Iceland covered with forest till mountains; but the forests were mostly birch, rather low, crooked and shrubby even then; and in a century they had cut and burnt 90% of those. Probably likewise in Greenland. While junipers do grow in Iceland and Greenland, there are absolutely no pines, spruces or other tall and straight conifers on either isle. Whereas Newfoundland does have those!
By 13th century, a problem with Iceland was that not only did Iceland depend on imports, but the ships were mostly built and operated by Norwegians. King of Norway could therefore tamper with trade of Iceland and, not owning the ships, the Icelanders could not easily do their own trade with Scotland or Ireland. Whereas heathen Vinland hostile to Norway would provide an alternative source for many imports OTL Iceland needed, and supply the ships so that Iceland could find alternative trade partners for other Europaean goods.
Even barring a civil war, by 976 Iceland was fully settled, maybe overpopulated. A population of 20 000 souls or so might send away a few hundred settlers every few years.
If by 1024, Greenland and Vinland have a substantial Christian minority tolerated by the heathen majority, and then a civil war breaks out on Iceland sponsored by Olaf Haraldsson, this can cause a backlash in Greenland and Vinland. From the point of view of heathens, the Christians of Iceland are ingrates who had generous concessions and broke the peace to invite a foreign tyrant. They might not persecute the Christian minority already in Vinland - on grounds that they are their neighbours and friends and unlike the Icelanders did keep their peace - but they may decide that any Christian from Iceland who has a reason to leave Iceland is guilty of his own plight and not welcome in Vinland.
As I mentioned, the Norse could explore far and wide. Several circumnavigations of Iceland, and Erik explored Greenland, giving directions for Western Settlement as well as northern hunting grounds, visiting which became a major part of Greenland economy.
From L´Anse Aux Meadows, what next?
Circumnavigating Newfoundland. The northeast coast with gulfs and reefs allows more farming and fishing settlements, trade with Skraelings and landfall for ships making a shortcut from Greenland.
But Belle Isle Strait will lead to more sheltered Saint Lawrence Gulf, western coast of Newfoundland and southern coast of Labrador.
Now, in the few decades after settling Vinland, Erik would have time to explore all around Saint Lawrence Gulf, and beyond on Atlantic Coast.
It seems to me that Cape Breton is a good place to settle. Cape Breton Highlands provide a visible landfall across Cabot Strait. Anyone who wants to go up Saint Lawrence River could go south and make a stop on Cape Breton - then turn west across Magdalen Islands or Prince Edward Island towards Gaspe Peninsula, instead of following Labrador coast and trying to pick a stopping place there. And from Cape Breton, the way southwest along Nova Scotia Atlantic coast is also open. The island has nice sheltered inland Bras d´Or lake, accessible for all the biggest Viking ships. Very fitting place for Norse settlement.