Gaara might save Naruto because he has changed due to Naruto's influence. Naruto taught him about the value of life and friendship. So, when Naruto is in danger from the Akatsuki, Gaara doesn't hesitate to risk his life. Also, the two villages, Konoha and Suna, have an alliance. Saving Naruto would strengthen that alliance and bring more stability to the ninja world.
In the fanfiction, Gaara may risk his life for Naruto because he sees a part of himself in Naruto. They both had a difficult past and overcame loneliness. Gaara knows what it's like to be hunted and feared, and he doesn't want Naruto to go through the same fate at the hands of the Akatsuki. Moreover, Naruto has always been there for Gaara in times of need, so Gaara wants to return the favor.
One reason is their friendship. Naruto was one of the first people to see Gaara as a person, not a monster. So, Gaara would feel indebted to Naruto and be willing to risk his life. Another reason could be for the sake of the ninja world. Naruto is often seen as a key figure in maintaining peace, and Gaara, as a responsible leader, would understand the importance of saving him.
Well, in many such fanfictions, Gaara might use his sand powers. He could sense Naruto is in danger through his connection to the sand or his own instincts. Then, he'd quickly move in, using his sand to shield Naruto from any attacks by the Akatsuki members, like blocking their jutsu with his powerful sand barriers.
One reason could be friendship. Gaara and Naruto have a special connection in the original story. In fanfiction, this connection could be deepened, and Gaara would save Naruto because he values their friendship. Just like Naruto once reached out to Gaara, Gaara would do the same for Naruto when he's in danger.
He could use his sand powers to create a barrier between Naruto and Sakura.
Maybe Sakura is being controlled by some dark force and is about to harm Naruto, so Gaara steps in to save him.
Well, a plot twist might be that Naruto actually gets captured by the Akatsuki while trying to save Gaara. Then, Gaara, in his weakened state, has to find a way to save Naruto instead. This would completely change the dynamic of the story. Or, it could be that the Akatsuki's real target isn't Gaara at all, but Naruto, and they use Gaara as bait. So when Naruto arrives to save Gaara, he walks right into their trap, but then uses his wits and new jutsu to turn the tables on the Akatsuki.
One reason could be that he has deep feelings for her. He might not be used to having such strong emotions for someone and this possessiveness is his way of showing how much he cares.
Naruto's character could develop in terms of his strategic thinking. Since saving Gaara from the Akatsuki is no easy feat, he might have to come up with more complex battle plans. This would show his growth from a brash fighter to a more calculating ninja.
One reason could be that Gaara, being a powerful and complex character, might have a different view on the concept of friendship. If he were to tell Naruto that his friends are only with him out of obligation or because of his status as a hero, Naruto might start to doubt his relationships and become depressed.
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.
Well, in fanfiction, if Naruto and Gaara joined Akatsuki, it would be a total chaos for the ninja world. Akatsuki's goals would likely be completely derailed. Naruto is all about friendship and protecting the village, and Gaara has also turned to the side of protecting his people. Their values would clash with Akatsuki's more malevolent intentions. Maybe Naruto would try to reform Akatsuki from the inside, and Gaara would be there to back him up with his powerful sand abilities.