In general, the early Medieval Norse people (often referred to as 'vikings') lived in a culture that was almost entirely oral - very little was written down.

Most of what we know are what Icelandic christian monks wrote down in the 13th and 14th centuries and undoubtedly coloured both by them and by the fact that Norde mytology, history and Sagas varied with regions, retellings, the teller and the audicence.

Norse paganism was never a centralised religion with doctrines, rules or tenets of faith to be adhered to - what Gods were worshipped varied with regions, seasons and the local situation. There are also theories that the Norse considered religion a local thing - thus it would be completely normal thing to be muslim in Moorish Spain and christian in France and Norse pagan in Denmark - because those God(s) ruled there, and switching between religion as you travelled would then be normal.

In general, christianity and the old Norse pagan beliefs co-existed for a long time - even after official christianisation, Norse paganism continued to be practised and slowly morphed into superstition and folklore. Magic rhymes read over mares to increase their fertility and make them become pregnant with foals included invoking the name of Oden as late as the 17th century in Småland in Sweden.

Norse paganism continued to be practised alongside christianity n Svealand and when Inge the Older wanted to abolish the traditional midwinter sacrifice to the Norse pagan Gods around 1080 he was deposed and his nephew Blot-Sven was elected King and conducted the traditional sarifices - despite the fact that a majority of rune stones erected carried christian crosses at this time.

The Norse of this time were also in general very relaxed about ethnicity - they had no qualms taking, buying and selling slaves of their own and other ethnicites.

Considering how relaxed the early Medieval Norse were about religion and ethnicity in this era, and how the Norse pagan faith did not have any centralised rules or guidelines on how and who could practise it, I would assume that most would just shrug and find it natural that someone switched to the local religion.