WARNING: The following contains spoilers for The Umbrella Academy Season 2, streaming now on Netflix.
Netflix's The Umbrella Academy Season 2 had the Hargreeves siblings scattered across the 1960s in Dallas, Texas after failing to stop the apocalypse in 2019. Unbeknownst to them, their presence there caused another apocalypse. This time, they banded together and prevented the end of the world but that doesn't mean they didn't alter the timeline in other ways. Given how many people they interacted with in the '60s, it shouldn't be surprising that they returned to a very different 2019.
As Five explains, when it comes to time travel, "no one is insignificant." In fact, his entire job at the Commission consisted of strategically killing people to keep the correct timeline intact. The Hargreeves may not have intentionally killed many people in the '60s, but they definitely made an impact on the ones they interacted with. As a result, there are several ways in which the Umbrella Academy may have screwed up the timeline.
Just their existence in the past was enough to alter time. Each of their arrivals was documented by a television salesman named Elliot, who believed they were aliens. Elliot appeared to lead a fairly normal life before witnessing the siblings' arrival but by the time he met Five, his wife had left him and he had become a full-time conspiracy theorist. He helped Five find his siblings and let them use his home as a meeting place. Because of this, Elliot was killed by the Swedish assassins who were after the Hargreeves. Who knows if Elliot had much of an impact in the grand scheme of things but if the siblings hadn't time traveled into his life, he could've met a drastically different end.
Following his arrival in 1960, Klaus accidentally started a cult after demonstrating his powers and giving people words of wisdom in the form of song lyrics that hadn't been written yet. He gained several dedicated followers, likely altering their lives forever. They gave up their lives and livelihoods to follow Klaus wherever he went. Additionally, he told them that world ended in 2019. Even when Klaus came clean about lying to them and tried to get them to return to their old lives, his followers continued to praise and worship him. Although Klaus returned to 2019 with the rest of the Academy, the cult carried on without him and was shown picking up the last Swede brother. Destiny's Children probably came to an end eventually but they could still have recruited more followers after Klaus left.
Later on, Klaus found his lover from the Vietnam War, Dave Katz, and tried to prevent his death by convincing him not to enlist in the first place. Unfortunately, his plan backfired and after their encounter, Dave's homophobic uncle made him enlist even sooner. In the original timeline, Dave joined the army where he later met Klaus. In the final episode, however, it is revealed that Dave enlisted as a marine, potentially changing his fate. Some are speculating that in the new timeline, he could have survived the war. While this would be a positive change for Klaus, it could also come with some unwelcome consequences.
After her arrival, Allison took part in the Civil Rights Movement. Through her work, she met and married local activist Raymond Chestnut. Since the movement was already happening without her, it's unclear whether her presence changed much. On the other hand, she undoubtedly changed Ray's life when she told him the truth about her powers and the future. Even if Ray kept this information to himself, it would probably influence his actions from then on. Again, this might not have messed with the timeline too much but there could still be repercussions.
Like her sister, Vanya fell in love with a local and changed the course of her life forever. Sissy lived quietly on a farm with her husband, Carl, and her son, Harlan. During Vanya's time with them, she accidentally transferred some of her powers to Harlan. This led him to accidentally kill Carl in an altercation and by the end of the season, Sissy and Harlan were fleeing to California. Vanya tried to take her power back in the Season 2 finale, but she didn't realize that Harlan retained some telekinetic abilities which he used to levitate a toy bird. Because of this, many now believe that Harlan could be connected to the Sparrow Academy, who made their entrance at the end of the season.
After finding out that Sissy and Vanya were having an affair, Carl had Vanya arrested and she wound up being interrogated by the FBI. After being tortured, Vanya lost control of her powers, killing multiple FBI agents in the process. While the siblings didn't stick around for the fallout, the deaths of several federal agents would surely draw significant attention from the government. It could even have had international implications considering they thought Vanya was a Russian spy.
Aside from Ben, all of the Hargreeves met with their adoptive father, Reginald. More than once, they asked for his help stopping the apocalypse and time traveling but to their chagrin, he refused. Many fans are now theorizing that Reginald's impression of the Umbrella Academy was so abysmal that it caused him to adopt different children, forming the Sparrow Academy. The only reason he still adopted Ben was because he didn't actually meet him. It probably didn't help that Diego broke him and Grace up. Grace wasn't around by the time Reginald adopted the Umbrella babies so their relationship came to an end some time before, but losing her in that way probably had a lasting effect on Reginald. He may not have even built a robot version of Grace to nurture the Sparrow Academy.
Finally, Five met his past self and after trying to kill each other, he gave himself the correct equation so the other Five could travel to 2019 without reverting back to his thirteen-year-old self. Luther also told him that Vanya caused the apocalypse, saving Old Five a lot of investigating. Since the Academy appears to return to a different 2019, this may not have affected their timeline. Instead, it could've created a new timeline in which Five stayed an adult and saved the world by being nice to Vanya.
Streaming now on Netflix, The Umbrella Academy Season 2 stars Ellen Page, Tom Hopper, David Castañeda, Emmy Raver-Lampman, Robert Sheehan, Aidan Gallagher and Justin H. Min, with Ritu Arya, Yusuf Gatewood, Marin Ireland, Jordan Claire Robbins, Kate Walsh and Colm Feore.