White supremicists & ANTIFA are the same brand of people with same type of hate
Side Score: 3
Our hate is different
Side Score: 2
Perhaps the scariest thing about ANTIFA is that they don't even do research into whether a person is actually a Nazi before attacking them. This was be seen when Luke Rudkowski, an anti-establishment journalist in the alternative media with a non partisan slant was assaulted by them at the G20 (Source 1).
Side: They are
The Horseshoe theory pretty much proves this, saying that the Far Left and Far Right are closer to each other than we think. And it's true
No it isn't. It's bullshit. Are the north and south poles closer together than we think? No, they are the furthest points apart in the Earth's spectrum, just like the far left and far right are the furthest points apart in the political spectrum.
The left is the antithesis of the right. The right believes in socio-economic hierarchy and the left believes in socio-economic equality. The only reason there even is a left is because Karl Marx wrote an exhaustive academic study about why hierarchical systems such as capitalism are unsustainable. He also warned that if anybody used violence or intimidation to implement communism it would lead to another form of dictatorship, which is probably where you are getting the idea from that the far left and far right are comparable. Communist societies are easier for a dictator to seize control of, but once this occurs they cease to be communist societies in the sense Marx intended. The regime of Stalin for example, was more like military fascism than Marxist communism. It created a complex environment where Russia identified economically with communist principles, but socially there was a party dictatorship reminiscent of Mussolini's Italy, or Hitler's Germany.
Side: Our hate is different
I think I see where you are going with this, and your discussion of how the USSR was leftist economically but far right socially/politically is where you touch on the problem.
The horseshoe theory is too simplified to work, and so is the standard right-left continuum. The problem is that, horseshoe or not, right and left apply to a 1-dimensional continuum when a 2-dimensional model is probably more useful, the dimensions being Politics and Economics.
Politically, Monarchies & Dictatorships are on the far right, and pure (non-representative) democracies are on the far left. The horseshoe theory does not work on this dimension because the degree to which power can be centralized really is on a straight one-track continuum, ranging from one person in charge to everyone equally in charge.
Economically, Communism and Socialism are on the far left, and feudalism on the far right, with completely free market capitalism in the center. Here, I would say that the horseshoe theory could work simply because the control/ownership of all goods and services is the government in both Communism and Feudalism; on neither end do individuals own anything, but in the middle (capitalism) the individual actually owns his/her own labor.
I do disagree that free-market capitalism is hierarchical, simply because individuals are free to sell their labor or the products of their labor to whomever they choose, and then reinvest the capital. In a pure free market (no subsidies or bailouts) the market enforces a pretty strict meritocracy based on multiple criteriachosen by the market not the government. This meritocracy, combines with individual ownership of one's own labor, to make free-market capitalism intrinsically democratic as opposed to hierarchical.
The individual ownership puts it outside of state-owns-everything systems, i.e., Communism/Socialism and Feudalism. If we wanted to, we could put Communism, Socialism, and Feudalism all on the right (because of the state ownership of everything), and put capitalism on the left (because of the total individual freedom, both as buyers and sellers), but that would require telling everyone their definitions are wrong, which would cause too much confusion.
Frankly, I would trade the horseshoe for three spokes (120 degrees out from each other) with communism/socialism, feudalism, and free-market capitalism each on their own spoke.
Consider that the US is politically center-left (generally non-authoritarian, non-hierarchical), but economically center (welfare state in free(ish) market capitalism). The Nazis were a leftist organization economically, but right of center because of the hierarchical dictatorship required to force people to give up what they earn to support those who did not earn it, it is necessarily politically autocratic, despite the use of a parliamentary system (in the German incarnation).
Side: They are
The KKK & Co are hateful & resentful of particular groups of people, as a result of buying into the identity politics, and "poor me" BS.
ANTIFA also buy into identity politics, but hate anybody (regardless of identity group) who says anything they disagree with.
Basically KKK & Co. hate people, but ANTIFA hates freedom, especially the First Amendment.
So, no, they are DIFFERENT flavors of a$$hole.
HOWEVER, White Supremacists (KKK, etc.) and Black Lives Matter (and groups with similar ID politics agendas) ARE the same brand of people with the same type of hate and irrational entitlement.
Side: Our hate is different