I'm an outsider so I don't know anything about Swedish politics. From the outside this comes off like one party I don't like winning an important election.
Is there anymore details you, or other Swedes that know what this is about, that could shed light on us heathens as to why this is such a terrible thing as to incur the "nazi" metaphor?
Their roots are literally fascist. You can draw a pretty straight line from 1930s swastika wearing swedish nazis through a series of failed parties and racist organisations to the founding of SD, the party he's talking about, in the late 80s. In the mid-90s they had to ban wearing nazi-uniforms to party meetings!
To be fair though, they have moderated themselves quite a bit since then, and purged many "real racists" from leadership roles, so they are becoming more and more sanitized, but they are still much more hostile to immigration than any other (significant) party in Sweden.