I was recently lucky enough to spend a few days in Iceland, and among other places, I spent some time at the National Museum and the Þingvellir historic site. At both places there were plaques/exhibits describing the traditional account of the adoption of Christianity, which I found (and which the exhibits themselves acknowledged) to be very unusual.
To give the very, very short version, Iceland in AD 1000 was said to be divided between Christian and pagan tribes, until at that year's Alþing it was decided by the (pagan) lawspeaker that the whole country should follow one religion and one set of laws, and that therefore Christianity should be adopted. With the caveats that pagan gods could still be worshipped in secret, and that the pagan practices of eating horsemeat and exposing newborns (!) would be allowed to continue, the various chieftains accepted the proposal, and Christianity was officially adopted peacefully.
At the National Museum, it was acknowledged that the story is very unusual amongst the accounts of the Christianization of other nations, and one exhibit even seemed to suggest it may not be accurate, but no alternative accounts were provided.
How much is known by historians about how the Christianization of Iceland actually played out, both before and after the Alþing of 1000? Do we know, assuming that the pronouncement at the Alþing did happen, how it was enacted at local levels? Has there been any challenge raised against the narrative of the peaceful and consensus-based conversion?
How much is known by historians about how the Christianization of Iceland actually played out, both before and after the Alþing of 1000?
The primary sources on this are Íslendingabók (1122-1133) and Kristni Saga (early 13th century). Íslendingabók is a brief historical transcript of Iceland, and the author, Ari Þorgilsson, did attempt to reliably document what was known of Icelandic history at the time, of which Christianization is a big part.
His version of the events match with what you describe. It was a relatively political decision and made with a very clear goal in mind, to keep the peace.
„En nú þykkir mér þat ráð,“ kvað hann, „at vér látim ok eigi þá ráða, er mest vilja í gegn gangast, ok miðlum svá mál á milli þeira, at hvárirtveggju hafi nakkvat síns máls, ok höfum allir ein lög ok einn sið. Þat mun verða satt, er vér slítum í sundr lögin, at vér munum slíta ok friðinn.
The above passage, directly attribute to Þorgeir Ljósvetningagoði Þorkelsson, the lawspeaker at the time, clearly shows the intention behind the directive.
A loose translation would be "I think it would be wise", he said "That we don't let those who disagree the most rule, but instead compromise between them, so both sides have their way, to an extent, and we all have one law and one religion. It will come to pass that if we break the law in two, we will also break our peace."
This does not mean that there was no violence or dissatisfaction related to the shift in religion. Kristni Saga details killings related to missionaries in Iceland, and the King of Norway had arrested pagan Icelanders abroad. It's also important to note that Þorgeir is clearly aware of the possibility that peace will break down if things don't get mediated, so it's not difficult to infer that while there was no outright warfare, there was definitely disagreement and tension in the society.
Additionally there was international political pressure. Both directly from the King of Norway, and through trade with Europe.
Do we know, assuming that the pronouncement at the Alþing did happen, how it was enacted at local levels?
I actually don't really know about enforcement. In the next century the infrastructure of Christianity, churches and clergy was slowly created and built up.
Has there been any challenge raised against the narrative of the peaceful and consensus-based conversion?
Well, yes, but you're misunderstanding the narrative if you think the process was entirely peaceful and consesus based. It was a political decision take to avoid outright civil war, but there is a lot of grey area between civil war and an entirely peaceful process. It is widely accepted there was significant tension between the factions.
Multiple sources also indicate that Þorgeir was bribed in order for him to make the decision to embrace Christianity.