Stipulated: This person believes things that we think are wrong, and we want him, ideally, to stop believing them.
I assert that shunning him is counterproductive with regards to getting him to stop believing these things. He is almost certainly aware of the public opinion of Nazis, and he evidently doesn’t care, so peer pressure is already shown not to work. Besides, truth is not determined by a majority vote, so if we act like our numbers are the major argument against the Nazi ideology, or whatever similar ideology this person subscribes to, it not only weakens our position in his eyes, but also leads us to forget the real reasons for what we believe.
We have at least four options:
1) We can make rules prohibiting certain beliefs. That prevents free, nuanced thought and truth-seeking, and prompts resentment.
2) We can shun people with those beliefs. That leads to a fractured society and more resentment.
3) We can do nothing. People will still do business with each other, but the culture will be fractured and no one will learn anything.
4) We can communicate respectfully with everyone. I had to learn how from scratch, because I would never merely tolerate a difference of perspective that I couldn’t understand. Most other people just ignore or avoid differences, until they can no longer afford to and panic because they don’t know how to resolve political or ideological conflicts.
All we really need to do is set a good example for the person, provide information on our own beliefs (sometimes unsolicited, but always accompanied by empathy rather than force), and chide him when his beliefs lead him to disrespect people (though he is likely to be less disrespectful than how he is treated by liberals).
Nazi is as Nazi does. The same goes for social justice warriors.