Who cares if they were convicted? That detail is shoehorned in here to make it sound like a good example when it isn't. Neo-nazis are not a protected class, and so the deli owner would be entirely within their rights to not hire someone on that basis, with or without a conviction on their criminal record.
And honestly how often do they get convicted of say, a hate crime, that might show up on a background check compared to the number of neo-nazis in the country with clean records, or who get acquitted, etc.?