White Supremacists are LEFTISTS
That's true historically and it's true right now
Leftists and the media (but I repeat myself) always assume that white supremacists belong on the conservative side of the aisle -- because white supremacism seems a lot like patriotism and it is undoubted that conservatives are the patriots. Leftists tend to despise the society they live in.
But there is in fact a great gulf between thinking well of your own country and despising other people and countries. The despising is the key. Leftists are the despisers and the haters. They despise everyone -- including people different from themselves.
History makes the matter crystal clear. The two great aggressive nationalists of the 20th century were Hitler and Mussolini. Both regarded themselves as entitled to invade and conquer "lesser" races and nations. But Mussolini was a prominent Marxist and Hitler named his political party as: The National Socialist German Worker's party, the Nazi party for short. There is absolutely no doubt that the two were well and truly on the Left of their day. Many Leftists in their era were antisemitic and believers in eugenics -- FDR for one. Hitler just applied German thoroughness to such ideas. It's just Soviet disinformation that Hitler and Mussolini were "Right wing"
And nothing much has changed. Just about all the mass shooters over the last few decades were Leftists. The moment news of such shooters came out, the media labelled them all as conservative or "right wing" and blamed the GOP for their ravages. In recent times you would think it was Donald Trump who pulled the trigger.
But, after people had time to look into it, it almost always emerged that the shooter had Leftist sympathies and ideas. Not all shooters had supremacist ideas but most seemed to have ideas not far from that. They certainly had big egos.
Conservatives are not supremacists. It is Leftists who want to rule everybody. Conservatives just want to get on with their own lives in peace. It is only to resist the authoritarianism of the Left that conservatives get into politics. It's just necessary self-protection.
I studied this matter for many years during my academic research career and I always found the same thing: There was no correlation between patriotism and negative views about racial and other outgroups. Being patriotic didn't make you a racist or any other "ist". See here and here and here and here