Maybe 'To Kill a Mockingbird' could be considered in a way similar. Scout and Boo Radley start as almost like strangers, but as the story progresses, their relationship changes. The novel shows how the town's perception of Boo as a stranger is wrong and how Scout comes to see him in a completely different light. Another one could be 'Anne of Green Gables'. Anne comes into a new place and family as a sort of stranger, but soon she becomes an integral part of the community and the relationships she forms are far from the typical 'stranger' interactions.
If the 'not as a stranger novel' is about characters quickly becoming more than strangers, then 'The Fault in Our Stars' might be relevant. Hazel and Augustus meet and almost immediately form a deep bond. They don't act like typical strangers would in such a situation. Also, 'Pride and Prejudice' has elements of this. Elizabeth and Darcy start as strangers with preconceived notions of each other, but as the story unfolds, they get to know each other beyond those initial stranger - like impressions.