Moreover, beliefs evolve over time and space - I wouldn't expect current adherents of religions to belief or worship exactly the same as people did a couple of centuries, much less millennia, ago, nor would I expect all contemporary adherents of any religion to worship exactly the same way either if distant enough for regional and linguistic variations to arise.
Regarding your main point, I agree. Different cultures who inherit cognate beliefs evolve differently.
A huge headache for Scandinavian archeologists is cognates like ‘Óðinn’ and ‘Wotan’, or ‘dvergr’ and ‘dwarf’, or ‘goð’ and ‘god’, or ‘tivar’ and ‘deity’, or ‘alfar’ and ‘elves’, mean different things to the distinct cultures. These cognates are false friends, as they say. Usually, the remoter Scandinavians preserve the ancient meaning, while the Romanized Hellenized Germans and English evolve different meanings because of different cultural contexts. When the Norse say ‘tivar’, they still mean the ancient meaning ‘sky beings’, and it includes both alfar and æsir, who are skyey phenomena.
What might be true for Germany, is sometimes false for Sweden. What might be true in (Saxon) England, is sometimes false for Norway. And so on.
English speakers often dont care what Scandinavians say about their own Scandinavian sacred texts. In my experience, German scholars are more cautious these days, but a century ago the opposite was true.
To this day, many English speakers still cannot grok that there is no such thing as a ‘priest of Þórr’. I mean after all, he is a ‘god’, isnt he? He must have a priest. There are no gods, there are no temples, there are no priests to run these imaginary temples.
Some Norse homes have a personal ‘shrine’ in their home, where they place food to share with a nature being. This is a mutual friendship with a particular phenomenon of nature.
But there is no organized religion. As one, archeologist put it, the Norse have no religion, but there are beliefs and customs.
Big culprits of the spread of this disinformation about Scandinavia were medieval German Christians. Like Adam of Bremen. This German Christian claimed there was a huge temple in Uppsala, where the Swedes practiced human sacrifice. When Scandinavian archeologists examined this claim, it turned out to be false. There was no temple. Nor evidence for it. Norse texts mention Uppsala and never mention anything like that. And of course, Adam of Bremen never actually visited Sweden. Wherever he got his rumor, the story is fiction, probably slanderous hatespeech by medieval Christians who are trying to eradicate vestiges of polytheism inside Germany.
A recent paper I read was by Norwegian archeologist discussing the use of horses in Viking Period funerary rites. The paper is surprisingly interesting. The burial of horses is frequent enough, yet absent from most archeological discussions. Focusing on this one thread, helped me get a better handle on what is going on with the remarkably diverse burial customs. Anyway, she had to discuss how the horse (sometimes) relates to Freyr. Because her paper was in English it was unavoidable to use the English terms. So she placed the term "god" in scare quotes. Those of us who know the Scandinavian archeology, we know that this word goð does not mean "god". But what can she do, she is talking in English. The enormity of the miscommunication is a universe away.
Heh, in the process of addressing the literature that did exist on the so far neglected topic of horse burial, she had to contend with a (to be fair from many decades ago) British archeologist who claimed that a tapestry in Oslo was a ‘high priestess’ who was worshiped by her followers as a ‘goddess’. *rolleyes*
Anyway. Headache.