Viewpoints on the Gods

The Gods don't cross water.

Neil Gaiman's American Gods provides a fantasy writer's perspective in that the people bring their Gods to the land they live on, it is a dance of culture & the environment. Personally I can't definitely answer the question, it relates to the Gods so who can say for certain!
From my own English perspective where the Gods have crossed from the continent to this archipelago my Gewessi view is that the landscape influences them as much as as it influences the people who live on it. I don't think the Saxon Ingwe is quite the same as the Danish Ingvi - perhaps the difference is like people. I am not quite the same person in work as I am in the pub.... The Thunor that I hear riding his chariot along the South Downs Way is not quite the same as the Thor who fights the Jotuns in Norway or Iceland.  The environment shapes us & our gods.
Whilst people may travel to all corners of the globe the spirits of the land do not
I state this on the Gewessi Path page it means that whilst Gods may travel the Land Alfs do not. During Blot I honour the Gods, the land Alfs and the Ancestors. Above I say that the Gods are also influenced by the landscape and that the people bring their gods with them as part of their culture but, like people, a new environment subtly changes them so that after several generations of integration and relationships with the landscape and it's land alfs they are something different and new. The Alfs do not travel and stay within the environment as they are an integral part of the land.

If I'm adopted I don't actually know my cultural heritage 

Yes you do, if you wish; it's your adoptive heritage - fostering and adoption are clearly mentioned in the Northern Tribes lore from the Irish books, the Welsh Mabinoigen and on into the Icelandic Sagas.  The gods are not genetically but culturally interested. The Icelanders are an interesting mix of mostly Nordic males with mostly British & Irish females (some willing but perhaps the majority less so).  These two cultures merged to create a unique cultural literary flowering based around a single set of gods.  This has influenced the whole modern fantasy genre.  Also DNA testing will make it possible to trace your ancestors route to where you are now. This would form part of the perennial psychological debate around nature (i.e. genetics) or nurture (i.e. adoptive parents). There is a balance to the two. Sometime nature overcomes nurture and sometimes the other way round.
The aim, in my opinion, of this path is to identify the positive and discard, or at least recognise and mitigate, the negative patterns & influences.  The Druidic philosophy suggests that your spirituality should enhance your life and the life of those around you. The Gewessi path says that you should use the 9 values as a set of values with which to improve your living environment.