The Bernie Sanders being a Communist accusation is actually a very good comparison.
People are pretty much saying. Bannon calls himself alt-right. White nationalists call themselves alt right. Therefore Bannon is a White nationalist.
It's just like saying, Bernie is a socialist. Stalin called himself a socialist. Therefore, Bernie is a Stalinist.
Clearly, Bernie and Stalin have different definitions of socialism and Bannon and the White nationalists have different definitions of the alt right.
except alt-right isn't just an umbrella term that happens to include white nationalists, it's literally synonymous with white nationalists
According to White nationalists' definition. Not according to other people's definition. According to people like Milo and Bannon, it is an umbrella term.
There is not some official National Alt Right Organization dictating what is and isn't alt right.