I have met Asatruars on both sides of this spectrum. The arguments that I've heard are as follows
1-The Nordic peoples are descended from the Aesir and only the Nordic people should be able to worship them (according to myth)
2-Humans are reincarnated along bloodlines so only those of Norse blood can worship the Aesir and Vanir
3-Heathenism is a purely European faith so only pure Europeans should be allowed in
4-Only the Nordic peoples can truly understand the Aesir and Vanir from a Nordic perspective
5-Since Asatru is so focused on ancestry and family people of other races will feel awkward participating in Heathen rituals
Really though if you look at the history of the human species you see that all these arguments are false. The Europeans are closely related to the Aryans of India. Most pagan faiths in Europe share striking similarities to each other and Hinduism. (not to mention all other religions around the globe) That takes care of point 4.
Now take the history out of it and look at the practices of most Heathen groups. Most Heathens and most pagans don't look at the myths as literal stories. They are stories that contain spiritual truths for those who have the eye to read them. So that right there rules out points 1 2 and 3.
Lastly during WWII Hitler toyed with the Norse faith and used it as propaganda. Those ideas trickled over to America and our own Neo Nazi groups. They adopted the Nordic faith and further mutilated it from its original form. Most Heathen groups allow members of other races and different orientations to join. However there are a few groups on the fringe who have adopted a very harsh bigoted approach to their faith. I believe the Odinic Rite is one of those groups but I'm not positive. Regardless of where the Kindred stands on the issue of race and orientation Heathenism is dominated by white people of European descent. There are quite a few LGBTs among the Kindereds I've met but very rarely has there been a non white of European descent. So in all honesty point number 5 can be valid to some individuals but it is a poor excuse to be racist and deny entry to people based on ethnicity or orientation.
There is a very similar argument floating around Hellenic circles. Some Greek Hellenes don't think that people descending from other European nations should be allowed to join the Hellenic faith. Since I'm of Norther European and Celtic descent I have an issue.
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But Hellenism unlike Heathenism has a very long and ancient tradition of xenophobia.
Personally I take a very global very Roman approach to other faiths. Synretism is another very ancient practice that many of the trad pagan faiths have conveniently forgotten.
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