Often, a battle or a common enemy can be the catalyst for their friendship in fanfiction. Let's say there's a new, powerful foe threatening both Konoha and Suna. Naruto and Gaara are forced to fight side by side. During this time, Naruto's unwavering determination and positive attitude start to influence Gaara. Gaara, in turn, shows Naruto his own strength and loyalty. This shared experience of facing danger together makes them respect and like each other, thus forming a friendship.
It could be the influence of a powerful enemy or a dark power. Suppose there is an enemy who has the ability to manipulate emotions or a dark power that corrupts Naruto's mind. This could lead him to change his personality and become more like Gaara. For example, if the enemy makes Naruto feel alone and unloved, he may start to develop the same cold and distant behavior that Gaara once had.