Heathenry has a far-right problem. It is not the whole of Heathenry and it is not a slander invented by outsiders, and the movement itself has been the loudest party in saying both things.
The reason is historical. The nineteenth-century recovery of Germanic antiquity was scholarly, romantic and nationalist at once, and by the early twentieth century parts of it had been absorbed into volkisch race mysticism in Germany and Austria. Heathenry did not inherit that deliberately, but it inherited the same material, and anyone reviving the gods of northern Europe in the twentieth century was working with sources that had already been put to that use. Some of the movement's founders reckoned with it and some did not.
The line is usually drawn between universalist Heathens, who hold that the gods call whom they call and that the religion is open to anyone, and folkish Heathens, who hold that it belongs by ancestry to people of northern European descent. Not everyone on the folkish side is a white nationalist, and folkish practitioners commonly frame the position as one about heritage rather than race. The distinction does not survive contact with the organisations that have taken the position furthest.
The documented case is the Asatru Folk Assembly. In 2016 it published a statement declaring, among other things, that it celebrated its "beautiful white children." Heathen organisations answered with Declaration 127, an undertaking not to promote, associate with, or do business with the AFA for as long as its policies stood. The declaration's own site records around 180 signatory organisations across more than twenty nations. The number is not arbitrary: stanza 127 of the Havamal instructs the hearer, when wrong is seen, to speak against it and give the wrongdoer no peace.
The Southern Poverty Law Center added the Asatru Folk Assembly to its list of hate groups in 2018, under a category it created for the purpose.
Declaration 127 has itself been criticised inside Heathenry for being aimed at one organisation rather than at a principle, which left it open to the objection that a renamed AFA would fall outside it, and later efforts have tried to state the commitment more generally. That is an argument about tactics conducted by people who agree about the substance.
What should not be concluded from any of this is that Heathenry is a far-right religion. The great majority of organised Heathen groups in Europe and North America are universalist, said so publicly and at cost, and continue to spend energy on a fight they did not choose.