TBH I've lost track of what is left or right wing now, and after Starmer's constant use of the term "far-right" I roll my eyes at the term. Knowing the difference between men and women is not far-right, nor harmful, nor hateful.
I think it's a fairly safe assumption to make that the killer opposed Kirk's views. The killer appears to have been terminally online, a former classmate described him as a Reddit kid. Now with all the celebratory nonsense put out online this week, it is that sort of stuff those terminally online kids consume which fuels their hatred.
There is a desperation by those who have fuelled the hatred not to "point fingers", but that has now moved onto pointing fingers at the same far-right they accused Kirk of being. When in doubt blame the far-right. Online memes are apparently far-right too.
Then you have trans ideology which revolves around victimisation, it overlaps Incel culture a lot, but without the criticism.
I can see a toxic mix of stuff here, but for some they don't want to look at their behaviour that influenced this nutter.
Call yourself far-left or far-right, whatever, but do not justify murder because of political views.