There is little in that article but innuendo.
The only quote from Bannon is that he said Breitbart had become "home to the alt-right". The alt-right is a pretty large, loosely defined group that does include some white nationalists, but it also includes mere anti-PC types and those who favor Western culture (being practiced by whites and non-whites alike). And even if Bannon believed that Breitbart had become home to extremely racist white supremacists, it doesn't follow that Bannon himself is one.
The only other documented fact in that article is that Bannon's ex-wife swore in court than Bannon didn't like Jews. Obviously, that's a statement by someone without much objectivity since she was in a divorce proceeding. We don't know if it's true, or if it has context, and we don't know how long Bannon said it. Maybe it was 20 years ago. But even if Bannon did say that over a decade ago, that doesn't mean Bannon is a "white nationalist" right now. Maybe Bannon has a legitimate religious disagreement with Jewish orthodoxy. Bannon is an Orthodox Christian and they're a bit more hard core than the Catholics and Protestants. Breitbart was founded by Jews, largely staffed by Jews, and has been consistently pro-Israel in its coverage. Dozens of Breitbart staff members, including Jewish ones, have said that Bannon has never shown any indication of anti-Semitism.
Bannon is a nationalist. This is not a secret. His nationalist instincts helped guide Trump to a victory in the election. It makes perfect sense for Trump to continue to heed his advice.