White nationalists do for obvious reasons, but not everyone within the "alt-right" movement does.  I'd argue that the vast majority are just trolls looking for a good laugh.  It's just that the media is desperately trying to cling to this racism narrative since they lost all credibility after this election.  

Neo-Nazi's tend to vote conservative, but that doesn't mean all conservatives are neo-Nazis.  Same with the alt-right.  The alt-right is a much larger movement that is particularly opposed to PC culture.