This is a quote from Wikipedia. If you don't like that source then feel free to share your own!
"Key to the far-right worldview is the notion of societal purity, often invoking ideas of a homogeneous "national" or "ethnic" community. This view generally promotes organicism, which perceives society as a unified, natural entity under threat from diversity or modern pluralism. Far-right movements frequently target perceived threats to their idealized community, whether ethnic, religious, or cultural, leading to anti-immigrant sentiments, welfare chauvinism, and, in extreme cases, political violence or oppression.[2]"
The KKK would be far right because they focused on the threat to society/their community from African Americans (and also Jews and other groups. But predominantly black). it wasn't a matter of black people just needing to assimilate. They would always be a threat to the purity of society, and the safety of women/girls
The EDL was not set with black people as the predominant enemy (although some members of the EDL also didn't like black people much). It's main enemy was religious. Specifically the idea that Islam was a threat to UK society and UK society and that "British Muslims" were effectively a threat from within. It's not far right to worry about, eg Islamic extremism or terrorism. Islamism is an extremist ideology in the same way that "Christianism" would be (foreshadowing). Where it tips into being far right is the idea that Islam in general is a threat, and that basically all Muslims are potential threats and a danger to UK society and cohesion. Is that fair to Tommy Robinson? In his own words
"By saying that he was sane, it gives a certain credibility to what he had been saying. And that Islam is a threat to Europe and the rest of the world"
So yes, SYL does consider Islam a threat to Europe. Which is far right.
(They "he" referred to in the quote by the way, killed 77 people in Norway. Most of them teenagers. I will say that while SYL approved of his theory, he at least publicly denounced his (violent) methods. So if you wanted to be really reasonable to him you could say SYL is a non-violent far right extremist whilst AB was a violent far right extremist. If you wanted to be less kind, you could quote SYL saying that "it would have been easier to justify if the crime were committed against Muslims". As that implies a quite unpleasant line of thinking. But if Stephen Yaxley Lennon was a non-violent far right extremist, he was surrounded by violent far right extremists... The Norwegian murderer was friends with numerous members of the EDL on Facebook, called the EDL his inspiration, and his killings were praised by other high ranking EDL members. Also other EDL members went on to be arrested for trying to bomb mosques. So the EFL was a far right organisation set up by someone who publicly talked about using democratic methods to achieve their aims (that's not the same as being pro-democracy. But whose members were open to extreme violence to achieve their aims.
It is.not far right to.think Islamic extremism is a threat. It is far right to extrapolate that out to over a billion Muslims. In the same way it isn't far right to be horrified by what the Norwegian serial killer did. But it would be to extrapolate that to all Christians (since he made "Christianism" a central part of his manifesto). There are violent Buddhist nationalists and Buddhist monks who have encouraged the mass murder of non-Buddhists. Most Buddhists are chill. There are lots of devout Muslims in the UK who care about their faith but are also basically nice people who, like most people just want to be left alone to live their lives. Just like Catholics, protestants, atheists, Jews. It's the rejection of that,.that is far right.
Even the kindest interpretation of Stephen Yaxley Lennon is that he is non-violent but still far right. I am trying to be as fair as possible and you can't blame someone for the actions of other people. But if this was, eg, a far left person who was repeatedly in the company of people who went on to do violent things, was on several different occasions cited as the inspiration for those violent acts and immediately after the atrocity "yes-butted" about the killer would you be so generous? The only way you could argue that he wasn't far right is if you refined what far right means.
The one argument against myself I can make is that SYL is good friends.apparently with Andrew Tate. Who is a mixed race convert to Islam. (He has also boasted about moving to Romania because it's easier to get away with rape there, has been accused of sex trafficking in Romania, has been accused of rape in the UK). Innocent until proven guilty and I know his supporters see Tate as unfairly targeted..Maybe SYL does too..but it's crazy to me that SYL apparently has a suspicion of all Muslims except the one famous for having multiple rape cases against him. But people are complicated and we may never understand how the human mind works.
But in conclusion. People describing SYL as far right aren't smearing him or unfairly believing mainstream smears. They might be older than you and remember all this shit.