In The Stranger, what are some ways in which Meursault seems normal and in conformity with society and ways in which he seems non-conformist?

Meursault conforms by engaging in human relationships
(Marie and Raymond) even though he tries to stay as emotionally removed as possible. He
also goes to a job every day. This is perhaps his most conformist practice since it
occurs every day and serves two main purposes: to benefit a company and to sustain
Meursault’s own way of life, which by his standards, is arbitrary. This shows that he is
not completely indifferent. He does certain things to continue his way of life. So, he
does find some significance even if it is to make arbitrary choices. Melville’s Bartleby
had a much greater (and less selfish) degree of scorn for conformity because he refused
everything.

So, I think you are correct. On the outside,
Meursault goes about his daily life as most people do. Although he is indifferent to his
mother’s death, he does the socially accepted thing by attending the funeral. He does
not mourn but he goes through the motions that society expects of
him.

Interpretations of this novel often point out that
Meursault exhibits the Absurd hero through his actions. But this isn’t always the case.
It really isn’t until the murder and the trial that Meursault’s outward actions begin to
represent his philosophy of Absurdity. In other words, this is when Meursault’s
indifference affects his external world. Then the external world threatens his
indifferent existence and he is forced to defend and explain himself. His testimony in
court and dialogue with the priest are the final examples where he actually shows his
nonconformity to the external world.