Discussions of John Updike's short story "A & P" often center on the coming-of-age theme as it plays out in Sammy's reaction to three girls in bikinis who walk into the A & P and his struggle with the store's manager, Lengel, over their treatment. Your interesting question shifts the focus from the coming-of-age theme to a Marxist reading of the power struggle between Sammy, a teenager on the cusp of adulthood, and Lengel, the unsympathetic, autocratic, and self-righteous manager of the A & P.
Because Marxist critics take their guidance from Karl Marx and his theories of the economic, political, and social repression of the working class by the middle and upper classes, a Marxist reading of "A & P" would most likely focus on two elements within the story: 1) the implicit and explicit repression of Sammy and the girls by Lengel and the authority he represents (including Sammy's parents) and 2) Sammy's own assumptions about class and power with respect to the leader of the three girls, Queenie. A Marxist critic would, therefore, ignore the coming-of-age theme as relatively unimportant when weighed against the struggle against explicit repression and implicit, but incorrect, assumptions about class.
When Lengel finally notices the girls as they attempt to check out, he chastises them for coming into the store dressed indecently (in his view), to which Queenie replies:
"We are decent" . . . [Sammy's interpretation begins] her lower lip pushing, getting sore now that she remembers her place, a place from which the crowd that runs the A & P must look pretty crummy.
Sammy is, of course, imagining that her reaction is caused by her sense of superiority, and a Marxist critic would note that Sammy's response here results from the unconscious repression of Sammy by Queenie and her class. Sammy implicitly includes himself in the "crummy" class that runs the "A & P," indicating his belief that he and Queenie are separated by unspoken, but powerful, class lines. More important, however, is that Lengel, in confronting Queenie and the other two girls as indecently dressed, has exercised authoritarian repression--he perceives the girls as indecent because they have flouted his arbitrary rules of decent attire for the store's patrons. The girls, through Queenie as spokesperson, view themselves as decent, that is, morally decent, a vastly different interpretation of what constitutes decency. A Marxist literary critic would see this as a classic example of the repressive class defining morality in terms of appearance rather than one's moral or spiritual makeup.
In a gesture of solidarity with the girls, Sammy finally tells Lengel that he quits, and Lengel's response is another repressive appeal to Sammy's sense of rightly-constituted authority:
. . . you don't want to do this to your Mom and Dad. . . . You'll feel this for the rest of your life.
Lengel, using a subtle form of repression, reminds Sammy that he has a familial obligation to his parents, who will be horrified by Sammy's act of anti-authoritarianism. An astute Marxist critic would likely point out at this point that Sammy, in an unexpected way, is now the least repressed individual in this story in that he has, for good reasons (sympathy for the girls and disgust at Lengel's arbitrary use of power) or for bad reasons (a case of raging teenager hormones), exercised complete freedom from repression.