Often, in fanfiction, it can bring them closer. They might start to understand Wanda better through watching her world in WandaVision. For example, Natasha Romanoff could see a side of Wanda that she hadn't before, a more vulnerable side, and it could strengthen their bond as female Avengers.
Some fanfictions might show that the Avengers become more divided. Maybe some like Clint Barton are more worried about the potential danger Wanda poses with her reality - warping powers shown in WandaVision, while others like Bruce Banner are more interested in the scientific aspects of what she's doing. Bruce might want to study it, while Clint is thinking about protecting the world from any threats. This could create tension between them as they argue about how to approach Wanda and the situation in WandaVision.
When watching WandaVision in fanfiction, the Avengers' relationships could also become more complex. For instance, Vision, being in a unique relationship with Wanda, could be a point of discussion among the Avengers. Some might be more accepting of their relationship, like Wanda's close friends among the Avengers. Others, who are more skeptical about the nature of Vision as an android and his relationship with a powerful mutant like Wanda, could be less supportive. This could lead to various sub - plots within the fanfiction where the Avengers' relationships are re - evaluated and changed based on their views of WandaVision.