Human attention is limited. Spending it on every controversy, rumor, or private detail can weaken one's work and judgment. حُسْنِ إِسْلَامِ الْمَرْءِ points toward the quality of faith expressed in disciplined conduct, not a need to comment on everything.
Finishing an entrusted task instead of arguing aimlessly, respecting privacy, and speaking clearly when speech is useful are practical examples.
In مِنْ حُسْنِ إِسْلَامِ الْمَرْءِ, connected possessive relationships convey “part of the excellence of a person's Islam.” The linked nouns contribute to the meaning as a whole.