Almost everything written about pre-Christian Inuit religion was recorded after Christianity had already arrived, and often by people committed to replacing it. That is the central problem with the evidence.
Christianisation began in Greenland in 1721 with the Lutheran Hans Egede, who set out explicitly to suppress the angakkuit, and continued with Moravian stations from 1733; by about 1810 essentially the whole west Greenlandic population was baptised. Moravians reached Labrador in 1771. Anglican and Catholic missions worked the Canadian Arctic later, reaching some central Arctic groups only in the early twentieth century, which is why the fullest ethnographic descriptions come from those regions.
The single most important body of material is the Fifth Thule Expedition of 1921 to 1924, on which Knud Rasmussen, Greenlandic-speaking and himself of Inuit descent, crossed from Greenland to Alaska and recorded at length from Iglulik, Netsilik, Caribou, Copper and Mackenzie Inuit, including extended conversations with the angakkuit Aua and Igjugarjuk. Franz Boas had worked earlier on Baffin Island. The material is unusually good for its period and is still the foundation of the subject. It is also a record taken during collapse, from a small number of named individuals, and generalising it across the Arctic is a known hazard.
Twentieth-century administration did further damage in Canada: relocation of families to assert sovereignty in the High Arctic, the killing of sled dogs during settlement, and residential schools, on which the Truth and Reconciliation Commission of Canada reported in 2015 with a volume on the Inuit and northern experience.
Nearly all Inuit today are Christian, predominantly Lutheran in Greenland and Anglican or Catholic in Canada, and that is not a veneer. The older framework nonetheless persists in ways easy to miss: naming practice, respect toward killed animals, and the authority of elders. Inuit Qaujimajatuqangit, the body of Inuit knowledge written into the governance of Nunavut since 1999, carries much of it into public institutions under a secular heading. Elders interview projects run by Nunavut Arctic College since the 1990s have published Inuit accounts of cosmology and shamanic practice, the first time much of this material has been set down by Inuit rather than about them.