It could be due to some fans' different interpretations of the characters. Maybe they see a certain chemistry between Sasuke and Karin in the original series that they want to explore further, even if it means creating a scenario where Sasuke cheats on Sakura. Also, fanfiction is a place for creativity and exploring different possibilities, and this is just one of the many extreme or different ideas that can come out of that.
I'm not entirely sure if it's a 'popular' trope. Some fans might be interested in exploring such dramatic and controversial storylines in fanfiction for the shock value or to explore different character dynamics. However, many fans of the original Naruto series who ship Sasuke and Sakura would likely be disappointed or even offended by such a concept.
In the realm of fanfiction, almost any scenario is possible. Regarding Sasuke divorcing Sakura for Karin, it may exist. Fanfiction authors draw inspiration from the source material and then take it in new directions. The idea might stem from Karin's past feelings for Sasuke and some fans' desire to see how such a relationship shift would impact the characters. It could also be a way to explore the characters' personalities more deeply, for example, how Sakura would cope with such a betrayal and how Karin would handle being with Sasuke in that context.
There probably is. Fanfiction writers like to take existing characters and create different storylines. But it's important to note that this isn't part of the official Naruto story. In the original, Sasuke and Sakura are a couple, and Karin has her own relationship with Sasuke which is more of comradeship in the official plot. Fanfiction just gives people the freedom to deviate from the original.
There could be. Fanfiction writers sometimes come up with very creative and sometimes controversial ideas. However, this particular plot would be quite a deviation from the original story's themes of loyalty and friendship. In the original, Sasuke has his own complex relationships that don't involve such unfaithful behavior in this way.
In some fanfictions, Sasuke and Sakura's relationship is often portrayed as a more developed romantic one. Sakura is usually shown as being deeply in love with Sasuke still, while Sasuke may be slowly coming to terms with his feelings for her. Karin's relationship with Sasuke is more complex. She has an unrequited love for him, which can create some tension. Karin and Sakura's relationship can range from being rivals to begrudging allies depending on the story.
Sakura might be heartbroken. She's been in love with Sasuke for so long. She could initially go into denial, thinking it's just a temporary thing. Then she might get angry and vow to prove herself to Sasuke, perhaps by becoming an even stronger ninja.
One reason could be that Sasuke realizes his true feelings for Karin were always there. Maybe in the fanfiction, he had some sort of epiphany that his connection with Sakura was more of a convenience or misunderstanding, while his bond with Karin was deeper on an emotional level.
Another way could be through his influence. Sasuke has a certain presence and leadership quality. He might make it clear to Karin that any harm to Sakura would not be tolerated. This could be through direct communication or by making it known in their group or among their peers that Sakura is under his protection.