In fanfiction, if Naruto hates the Uzamaki clan, it could lead to him making some extreme decisions. For example, he might distance himself from any Uzamaki - related matters, which could have a negative impact on the clan's growth and development. His hatred could also attract enemies who want to take advantage of the division within the Uzamaki clan. Moreover, it could change the power dynamics in the Hidden Leaf Village as the Uzamaki clan is an important part of it. His negative feelings might also make it difficult for him to pass on the Uzamaki traditions and knowledge, which could be a great loss for the clan and the village in the long run.
One possible consequence could be that his relationships with other characters who are related to the Uzamaki clan, like Hinata (since she marries into the Uzamaki family), become strained. It might also lead to internal conflict within himself as he battles with his own identity and heritage.