Funny, in the link you posted Woods in no way distanced himself from the League of the South, nor denied he was on its board, nor in any way repudiated its overtly racist statements. All he said was, "Yep, he found out about it."
I’ve addressed this issue at length in a Feb. 19 entry on the LewRockwell.com blog
I would have expected you would be able to go to Rockwell's site and pull up the information but I'll put the very end of it here for you. But I would recommend giving the whole statement a read to get even more insight
For these and for no other reasons, and in this context, have I had an intermittent membership in the League over the years. I have played no day-to-day role in the organization and I am responsible neither for the comments of any other member nor for the politically incorrect statements I am told can be found on the League's site. With the passage of time the League has begun to emphasize the importance of preserving Anglo-Celtic heritage, a position I am expected to repudiate. As an Armenian and not Anglo-Celtic at all, I nevertheless see no reason to: why should every group except Anglo-Celts be allowed to preserve their culture? (As for the group's "racism," a word that is thrown around at anyone who looks cockeyed at Jesse Jackson, I find it revealing that white supremacist organizations have repeatedly and vocally condemned the League.)
That should be more than enough to satisfy anyone's curiosity.