Earlier quoted context omitted.
"right wing" or "far right wing". Remember we're talking about literal neo-nazis here, not just Conservatives.
That's not how it goes in practice. The fact that the people in that twitter thread endorse antifa shows that they are either ignorant of what antifa actually is (as opposed to what it claims to be), or they endorse an organisation that is more fascist than the fascists it purports to fight.
It's possible to make generalisations across all the various groups, but you're going to have huge variance across them -- in pretty much all areas, including internal structure, attitude towards violence and political positions.
Of course groups are aware of one another and cooperate (as well as conflict, I assume) in an anarchic way, but there is no centralized power or executive. It's certainly not a single organisation.
From an organisational perspective, sports fan clubs are rather similar (mostly independent of one another, mostly local, very heterogeneous in how they work internally and interact with the world).