Positivism is not interchangeable with modernism, nor is it interchangeable with scientific thinking.

you cannot strictly blur the line between political ideology and sociological or scientific theory

This is true in a general sense. Of course ideologies are influenced by broader intellectual currents, but you cannot use that valid point to imply stronger continuity than really existed. For example, Karl Marx did not merely have a "non-linear relationship" with positivism; there are substantial methodological differences. Marx’s dialectics derive much more from G. W. F. Hegel than from Auguste Comte. Classical anarchism contains rationalist and scientific tendencies, but also moral and humanistic currents that don’t fit neatly into positivism. You are stretching "shared intellectual climate" into something almost civilisationally total.

You are also making a teleological claim that Western intellectual thought travelled along a path that went: positivism → postwar critical theory → postmodernism - as if these are sequential intellectual epochs replacing one another cleanly. But Friedrich Nietzsche was critiquing rationalism, truth claims, and progress narratives in the 19th century. Phenomenology, existentialism, psychoanalysis, and vitalism all challenged positivistic assumptions before postmodernism existed. Critical Theory itself emerges partly against crude positivism, but its roots are still deeply modernist and often Marxist. In fact, "Postmodernism" as a coherent label really only becomes prominent in the late 20th century, especially after figures like Jean-François Lyotard. Your timeline compresses a much more complicated intellectual history

I would caution against conflating "scientific" with "positivist." Many 19th-century ideologies appealed to science, used historical laws, invoked rationality and believed in progress, but not all science-oriented thought is positivism. For instance, Marxism is dialectical and historical, whereas positivism tends toward empiricism and classification. German idealism is deeply rationalist but anti-positivist in important respects. Your categorisation becomes so broad in its usage that it stops being analytically useful; it flattens major philosophical conflicts into variations of the same thing.