The question is "What does “far-right extremist” mean?"
That's a very difficult question to answer objectively. The user is asking for an "exact definition" of a term which is defined differently by different people. "Political extremist" is a heavily loaded term in general. Calling people extremists can be just an ad-hominem attack to discredit political opponents. Or it can be warranted. But anyone accused of extremism will usually protest being labeled that way, no matter if it is warranted or not.
If someone would have posted this question today, I would have closed it as "primarily opinion-based". But the question is from the time before I was a moderator and already has several answers. So it's too late for that now.
The problem is that your answer begins with "I think the only consistent answer is..." and continues with a wall of text.
Well, what if I think differently?
- Maybe I think your definition goes too far?
- Maybe I think your definition doesn't go far enough?
- Maybe I disdain people which I call right-wing extremists, but my reasons for hating these people center around aspects you didn't even mention?
- Maybe your definition applies to me, but I don't consider myself a far right extremist and now I feel you are mislabeling me?
- Maybe I am in fact one of the few people who self-identify as far right extremists, but I don't feel that your description represents my views accurately?
Well I could start a discussion in the comments, but I learned that Politics.SE is not a discussion forum. So what else do I do when I disagree with your definition? I downvote your answer and upvote one I agree with more.
That's why you should avoid answering opinion-based questions in general: they are a minefield of politically motivated voting. If you do decide to answer them, try to not answer them with your own opinions. You could try to answer them by quoting the opinions of relevant political scholars or definitions used by relevant political organisations. You should also try to provide a balanced picture which contrasts different definitions and highlights their differences.