[David] Roediger describes how the [post-civil war u.s.] anarchist movement, epitomized by [Lucy] Parsons, failed to respond to the Black freedom struggle. Similar to individualist anarchists, the anarchists of this period, according to Roediger, made overtures for the rights of Black people while remaining in a class reductionist perspective overall. Lucy Parsons attributed the racial violence of the period to class interests in a typical class reductionist and Marxist sense. According to [Steve] Shone, “Lucy often characterized racial problems through a Marxist lens, stressing class rather than race as an explanation for ethnic conflicts and exploitation” (Shone, 2010:70). Shone cites various scholars, including Robin D.G. Kelley, who describes her as operating within the confines of white socialist thought. Roediger also touches on her relationship to race; he recounts how Lucy said that “outrages” were heaped upon on the “negro,” not because he was Black, but rather because “[...]he is poor. It is because he is dependent.” Lucy Parsons chose actively not to identify as Black but rather as Mexican and other backgrounds.

Roediger also describes how Albert Parsons's analysis of race failed in part due to his frequent comparison between chattel slavery and wage slavery (2016:205-206). According to Roediger, Albert agreed with Jefferson Davis that wage slavery was a more effective way to exploit Black workers. Though it is clear that the Parsons were both committed to projects that were anti-racist, the anti-racism they espoused came second to their class politics. There was no acknowledgment of the Black struggle as important as or relevant within – let alone primary to – the organized labor struggle.

— Black Anarchism and the Black Radical Tradition by Atticus Bagby-Williams, Nsambu Za Suekama (Moving Beyond Capitalism --Now!) (Page 13)