The US left do advocate for something resembling weak ‘equality of outcome’ in that poor and ill aren't thrown under the bus. However, while the left can be seen as reducing personal economic freedom, the oppression of social freedoms is a purview of conservatives. So ‘Harrison Bergeron’ is closer to a parody of a right-wing dreamland. Perhaps incels would in fact welcome an ‘equal outcome’ social world, where they are on the same level as Chads.
The story itself is pretty light on discussing any specific norm (other than maybe gender, but I think that just wasn't on the author's radar), whether economic or social, but it does tackle the general sense of 'master' vs. 'slave' morality as described by Nietzsche, which is somewhat perpendicular to the left-right spectrum and shows up at both of its ends. Harrison is parodied as the extreme 'master' who justifies seizing power as a natural birthright deriving from his absurd set of qualities, and the government is parodied as the extreme form of 'slave' morality where nothing counts beyond the good intentions of people and any form of competence is seen as dangerous and unfair.