Risking to fall for a troll here… Nazis very much exist. There might be the term neonazis to distinguish them, but lets face it. The neonazis are identical in their ideology, political means (threats, violence, murder), demeanor and even in appeal they try to be as close to the original as possible.
For the second part. Do you think a Nazi will discuss openly with you? No they would murder you in place, if you dont follow their ideology, or heck even if they just think you looked at them funny. Giving them space in public and letting them influence public space is affirming their positions and supporting their means to influence society. That is where the “punch a Nazi” is coming from. They need to be denied public space and public power. That is also where some realise they are not in the right, because the public is not agreeing with them and not secretly supporting them, which is a cornerstone of their belief system.