> I'm skeptical that any such job exists.

The University of Oslo has a "Center for Research on Extremism" (CRE-X). https://www.sv.uio.no/c-rex/english/

While their name suggests they might be just as interested in the far-left as the far-right, if you look at their actual publications, they are almost entirely focused on the far-right, and even those rare occasions they do pay any attention to the far-left, it is generally cases of far-right/far-left overlap. So yes, they are an example of people researching far-right extremism for a living.

In fact, there are lots of other university and independent research centres looking into the topic–I cited CRE-X as an example only because they were at the top of my Google search results. It is something government research funders in many countries want to invest in, and there are also various wealthy philanthropists and charity/activist/lobby groups willing to put money towards it. Nothing unbelievable about someone claiming to do it professionally, because people do.

Lots of people work in this space. How do you expect anyone to write or teach about such a topic without performing research? Keeping an eye on 4chan/pol/ is the least interesting part of my work, because while it's the largest community of its type it functions mainly as an amplifier/dumping ground rather than a source of much original content. /g/ is a much more enjoyable community to participate in.