Readers of the manga were quick to notice that Gaara's violence was significantly cut in the Naruto anime - here's why. In both mediums, the future Kazekage was eerily portrayed as a source of terror to enemies and allies alike during his younger years. However, the Naruto anime's depiction failed to capture the gruesome brutality of Gaara's that was initially illustrated in the manga.
Gaara was first introduced to the Naruto series at the beginning of the Chunin exam arc. In a matter of a few chapters, Gaara threatened to kill his siblings, shattered Rock Lee's arm and leg, attempted to assassinate Rock Lee, and successfully assassinated many others by crushing them in a sand sarcophagus without a single showing of mercy. Thanks to the stylized artwork drawn by Naruto's creator Masashi Kishimoto, Gaara's actions were depicted in ghastly gory detail. The anime made the conscious decision to remove these details.
From a production standpoint, the violence in Naruto had to be dialed down due to its appeal as a kids' television show. Especially in the west, the production team had to make some major adjustments to Naruto's action sequences in order to achieve the coveted TV-PG rating. Gaara's merciless actions just happened to be a byproduct of this censorship. However, this change served to benefit Gaara's character arc in Naruto from a storytelling standpoint. In the manga, Gaara was portrayed more as a ruthless villain. Though his backstory did illicit some sympathy, his cruel attacks were hard to overlook. By subduing all the violence in the Naruto anime, Gaara's ruthless attacks were less pronounced. As a consequence, Gaara became a more redeemable individual from the start.
Gaara was Naruto's foil. Both grew up completely isolated in their respective villages due to being jinchurikis: humans containing a monster sealed within. The villagers' fear of such monsters was expressed through acts of disgust and avoidance directed at the unaware children. Not knowing the cause of this mistreatment, Gaara and Naruto began to develop feelings of rage and hate. However, while Naruto was able to combat his negative emotions by establishing meaningful relationships with characters like his father figure Iruka, sensei Kakashi, and teammates Sasuke and Sakura, Gaara still had no one. The series' goofy protagonist could have easily become Gaara under different circumstances. Viewers wanted to watch Gaara be redeemed, because they would have wanted Naruto to be redeemed had their roles been swapped. Keeping Gaara's viciousness in the anime would have tainted any comparisons to Naruto, thus making support for his redemption much more difficult to achieve.
Though the Naruto anime noticeably changed the extent of Gaara's violence, his character arc remained relatively the same. The lonely boy who used to take his bloodlust out on the world became a beloved leader devoted to protecting his home. Whether or not the Naruto anime's censorship was necessary may be debatable, but both mediums managed to effectively show the growth of an otherwise fan favorite character.