Psuedo/Synth left

 from here : "Firstly, the language of Left and Right is foreign to classical Marxism, which interpreted social contradictions in terms of objective class antagonisms, not with regard to the subjective differences of the political compass. 

Secondly, Left and Right only emerged historically as the relative poles of bourgeois democracy, whose parliamentary terms only came into being and spread across the capitalist world to naturalize the bourgeois system of government. 

Lastly, I emphasize how Marx’s theoretical originality manifested through a ruthless criticism of the left-wing politics of his time, namely, the various bourgeois and utopian schools of socialism and anarchism against which he sharpened his historical analysis of class society. Marxism, in my interpretation, gains its critical force by demystifying the Left’s habitual idealism, moralism, and utopianism, unhistorical tendencies marking the Left of Marx’s time and our own."

BUT as its above-linked About page states, its political heritage includes the revisionist, petty-bourgeois "New Left" movement of the 1960s-70s, which of course is associated with critical theory and idpol more generally. In other words, this organization is not genuinely Marxist and therefore by no means an authority here.

"the language of Left and Right is foreign to classical Marxism"

Even if we grant that this language is foreign to classical Marxism, this does not mean it is excluded from orthodox Marxist works—that is, those published after Karl Marx's death (1883) by great thinkers including Frederich Engels, Georgi Plekhanov, Vladimir Lenin, Leon Trotsky, and Rosa Luxemburg. Indeed, Frederich Engels uses this language in Ludwig Feuerbach and the End of Classical German Philosophy (1886):

The Left wing, the so-called Young Hegelians, in their fight with the pietist orthodox and the feudal reactionaries, abandoned bit by bit that philosophical-genteel reserve in regard to the burning questions of the day which up to that time had secured state toleration and even protection for their teachings. (bold added)

Additionally, as Vladimir Lenin writes in The State and Revolution (1917):

To the Right of Kautsky in international socialism, there are trends such as the Socialist Monthly in Germany (Legien, David, Kolb and many others, including the Scandinavians Stauning and Branting); the followers of Jaurès and Vandervelde in France and Belgium; Turati, Treves and other representatives of the Right wing of the Italian Party . . .(bold added)

Finally, in In Defense of Marxism (1939/1940) Leon Trotsky observes:

In both of the documents mentioned in the above letter, Shachtman revealed excessive adaptability toward the left wing of the petty-bourgeois democrats – political mimicry – a very dangerous symptom in a revolutionary politician! (bold added)

"interpreted social contradictions in terms of objective class antagonisms, not with regard to the subjective differences of the political compass."

The terms "left-" and "right-wing" refer not only to subjective views, which of course are ultimately rooted in the material basis of society, but also the objective function of concrete politics. I expand on this point below:

You have an idiosyncratic misconception of what the terms "left-" VS "right-wing" denote. As I explain here:

Broadly speaking, political conservatism refers to efforts to maintain (or "conserve") the status quo, whatever it may be. Since the first class societies formed some 10,000 years ago and generated widespread economic and general social inequality, conservatism has been characteristically anti-egalitarian; it has henceforth functioned to maintain this highly unequal state of affairs.

...and here:

The term "right-wing" (conservatism) is variously defined as "the view that certain hierarchies are inevitable, natural, normal, or desirable

"a political and social philosophy whose central tenets include tradition, hierarchy, and authority

"the intellectual justification of inequality and privilege, and the political justification of the authoritative relationships such inequalities and privileges demand," etc.

Conversely, "left-wing" is defined in such ways as politics that "supports social equality and egalitarianism, often in opposition to social hierarchy," "the most liberal and egalitarian element of a political party or other group," "the political spectrum associated in general with egalitarianism," etc.

To be sure, left- VS right-wing politics are contradistinguished vis-à-vis their position on equality, with the former advocating it and the latter instead promoting hierarchies. 

Karl Marx’s theoretical originality manifested through a ruthless criticism of the left-wing politics of his time, namely, the various bourgeois and utopian schools of socialism and anarchism

Like all other apparently left-wing anti-Marxists, these tendencies are pseudo-leftist rather than genuinely left-wing. This quote from the World Socialist Web Site article "What is the pseudo-left?" is apropos here:

The pseudo-left is anti-Marxist. It rejects historical materialism, embracing instead various forms of subjective idealism and philosophical irrationalism associated with existentialism, the Frankfurt School and contemporary postmodernism.

The pseudo-left is anti-socialist, opposes class struggle, and denies the central role of the working class and the necessity of revolution in the progressive transformation of society. It counterposes supra-class populism to the independent political organization and mass mobilization of the working class against the capitalist system. The economic program of the pseudo-left is, in its essentials, pro-capitalist and nationalistic.

The Liberal 2.0 Anarchist Anti Tankies at their McCarthyist fandom Tankie.Fandom are an example of Synth left .Tankie.fandom is an echo chamber of reactionary bastardizations of marxism, mixed with ultra left (including the type mentioned here) which have interpreted the information and situation in a purely undialectical way.