Naruto is one of those few Shonen anime with a cast that always has something to offer when connected to their past, backstories, and lineage. With Naruto himself being an Uzumaki, fans were in disbelief after realizing that Tsunade, the granddaughter of the first Hokage Hashirama Senju and Mito Uzumaki, was in some way related to Naruto by their Uzumaki bloodline. No, Gaara‘s red hair is not a hint of him being an Uzumaki. While he does have red hair, it is not a direct indication of him being a part of the Uzumaki bloodline.
Similarly, fans of the series were left in disbelief once they learned that two red-haired characters in the series, Nagato and Karin, were both Uzumaki. Something to note was how neither of them had their last names revealed initially, following which their descent was revealed.Similar to Gaara, there have been several red-haired characters in the series, such as Otogakure Kunoichi and Sound Four member Tayuya, and Kumogakure Kunoichi and Team Samui member Karui, both of whom have no relation unveiled to the Uzumaki clan.