Most of the time, child abandonment isn't exactly a good look. Parents are responsible for their kids' well-being up until the point where they're able to fend for themselves, and those who shirk that responsibility typically deserve some criticism. But just like in real life, some anime parents who abandoned their children have pretty good reasons for doing so.
Some of these absentee parents intentionally sacrificed their lives for their children and community's benefit, as is the case with Minato Namikaze from Naruto and Grisha Jaeger of Attack on Titan. Others, like Fuu's father in Samurai Champloo and Thors Snorresson from Vinland Saga, had to leave their kids to avoid them being harmed by association with them. Still, others were just incredibly busy with saving the world or trying to take down the government, and had to leave their kids to get that done - Monkey D. Dragon of One Piece and Van Hoenheim of Fullmetal Alchemist are popular examples of this.
Vote up the parents who you think were justified in leaving their kids, and vote down those who you think should have stuck around anyway.
When Kushina Uzumaki is trying to give birth to her son Naruto, she's suddenly attacked by Obito Uchiha - claiming to be Madara - who wants to use this an opportunity to capture the Nine Tailed Fox. He succeeds in doing so, unleashing the beast to rampage through the town, destroying thousands of lives. While Kushina stands little chance of survival due to the trauma of both childbirth and having the Tailed Beast extracted from her body, Minato could have made a choice that would allow him to be in his son's life - that would be sealing the Tailed Beast back into Kushina's body so that it would be destroyed when she passed.
Instead, he chose to sacrifice that opportunity because he knew that Konoha would need the power of the Tailed Beast in the future. Instead, he used the Dead Demon Consuming Seal in order to half the chakra of the Nine Tails so that it could be sealed into Naruto's body, ending his own life in the process. He left his child orphaned for the good of Konoha.
Van Hoenheim didn't want to leave his family, but when he discovered that Amestris was in danger of being wiped out in the same way that his hometown of Xerxes was, he makes the painful decision to take off. He thought that this would be okay, because he was leaving his sons Edward and Alphonse with their mother Tricia, who he implicitly trusted with their well-being. Tragically, during his ten-year absence Tricia became severely ill and passed away, leaving his sons orphaned.
The two didn't take their orphan status lying down - instead, they tried to use alchemy to bring their mother back to life. This not only failed, but cost Edward a literal arm and leg, and cost Alphonse his entire body. When the boys recover, they leave on their own journey, burning their house down with the intention of never returning. When Van Hoenheim returns, he has a hard time reconnecting with his kids - even though they understand his reasoning to a degree, it doesn't change what happened to them while he was gone.
Fuu's father, who is known in Samurai Champloo as the Sunflower Samurai, abandoned his wife and young daughter for reasons that were not made clear until later in the series. Fuu describes him only as smelling like sunflowers, and finding him is the mission that drives her throughout the series. As it turns out, the reason why he left his family to fend for themselves was because if he did not leave, their lives would be at risk. As a Christian in isolationist Japan, he stood a very real chance of being executed along with his family if he didn't hit the road. To protect himself and his loved ones, he had little choice.
Grisha Jaeger was going to have to abandon his kid within the first thirteen years of his life no matter what - as a Titan shifter, he has a limited lifespan. He decides that he wants to make sure he passes on his ability to his son Eren, so he injects him with a serum that transforms him into a mindless Titan. When Eren inevitably eats Grisha, he becomes human again, but possesses the Titan shifting ability. Grisha knew that this was one of the few ways that his son could protect himself - though if he could have explained a little more about what was going on, that would have been ideal.