The use in religious context is an Abrahamization of Norse culture.
The first public record of the term “goði” is found on the Nordhuglo Rune Stone from Norway dating back to around 400 AD, as well as three other stones from Funen in Denmark. The word is used in opposition to gandr, which refers to a magic staff, and thus magics, believed to be the exclusive jurisdiction of women. In this context, the word “goði” therefore refers to a man who stays away from magics - as he should - and is as a result a good leader.
The term “goði” is also later documented in Landnámabók (Icelandic laws implemented following settlement by the Norse in the 9th century), as well as Grágás (Icelandic laws in use until integration with Norway in 1264), and refers to a secular community or military leader. “Goði” is indeed synonymously used with “höfðingi”, which refers to a chieftain or military commander. Subsequently, “goði” (or “höfðingi”) became voting members of Lögrétta, the legislative section of the Þing (assembly), and also nominated judges for trials. Free landowners, referred to as þingmenn, were required by law to be contractually associated with a “goði”. Goðar had jurisdiction over an independent goðorð, which could be traded, bought or inherited. However, if a female was to inherit a goðorð, she was required by law to hand over leadership to a man, making the position of goði de facto and de jure only open to men.
During Christianisation of Iceland, the Church started associating the term with religious duties similar to that of a priest or parish leader, encouraged by by the term’s similarities to the word “goð”, and hoping to facilitate conversion of Pagan leaders to Christianity.
The goði system was subsequently abolished by Hákon Hákonarson (Håkon Håkonsson in Norwegian, also known as Haakon IV) of Sverreættin (House of Sverre, Sverreættan in Norwegian), that is now Áskunnrættin (House of Áskunnr), following the integration of Iceland back into the Kingdom of Norway. Hákon Hákonarson wanted indeed to reduce the influence of the Church in Norway. As a king, he was very aware of the toxicity of Christianity, after the Church had attempted to kill him as a child (through the Baglarr), before he was eventually saved by Birkibeinar.
Ultimately, despite the attempts by the Church to Christianise the term, including in the writing of various texts, Goðar never were religious leaders in Norse culture, and any association of the term “goði” with religion is an Abrahamization of our culture.