What Banner says about changing the past is true, but the end result is false.
Banner tells the group you can't change the past because it's already happened, so what you're trying to alter is actually your future. So if the group went back and stopped Thanos from wiping out half the Universe, then the events that led up to them going to the past would never have occurred, i.e., The Hitler Paradox. That's basically saying you can't change events that you were a part of, or events that affect you; e.g., I go back to 1989 to warn my parents about my sister dying from meningitis. I was conceived 2 months after she died, so preventing this would either erase me from existence, or create a Hitler Paradox because I'd have no reason to go back to the past; that is, unless I stabilise the timeline by creating a Predestination Paradox/Temporal Causality Loop by leaving a message in the past to be read by me in the new timeline instructing me to go back to September ’89 in April 2024, warn my parents, and leave the message in the past, therefore closing the loop.
The outcome of the movie has some major flaws because, despite retrieving the Infinity Stones from the past, several things happened in the past that would make it so that what we see at the end of the movie should be erased from existence. When 2014 Thanos and the 2014 Black Order are brought to 2023 by 2014 Nebula, they're all killed when Iron Man snaps his fingers and they never return to their own time period, so anything involving Thanos and the Black Order between 2014 and 2018 should no longer exist – such as Loki, Heimdall, and Gamora's deaths. Plus Steve staying in the past erases the events of Agent Carter, plus all the events involving Peggy Carter that we've seen throughout various films.
If this were "The Flash", I'd say Time Remnants. However, based on what happens in the end, we're either looking at a timeline that, once time catches up, it will cease to exist, or the timeline has been split. So much was changed in the past that a lot of what we've seen between phases 1-3 should no longer exist. Examples:
When Marty goes back to 1955 and stops his parents' first meeting he endangers his own existence. Fortunately their first meeting is a fluxed point, it's their first kiss at the Enchantment Under the Sea Dance that's the fixed point that ensures Marty's existence. So he was able to ensure it happened, and Marty returned to 1985 twenty minutes before his Time Remnant goes back in time. However due to his parents coming together under different circumstances, Marty returns to a future with a different history to the one that he knows due to his actions in the past, so in order to keep this new timeline intact the Doc has to ensure that Marty's Time Remnant goes back in time creating a Predestination Paradox/Temporal Causality Loop.
When Barry goes back in time to get information from Eobard Thawne, his plan to keep the Timeline safe goes wrong due to a Time Wraith. He ends up having to reveal himself to the past versions of his teammates, and his past self. Fortunately what Barry changes in the past are all fluxed points so they're no threat to the timeline. However he returns to a future different than the one he came from. He returns to the future moments after he left, but when he returns, Cisco, Caitlin, and a reformed Hartley Rathaway are there waiting to combat the Time Wraith. Again creating another Predestination Paradox/Temporal Causality Loop.
As for Avengers: Endgame, the changes that are made in the past don't effect the present in the slightest except Thanos learning what is destined to happen with the Infinity Stones.
Due to Lang causing Stark to go into cardiac arrest, Loki ends up escaping with the Space Stone, so how long would Thor have been stranded on Earth? And how long would it of been before Loki was captured? Without the Space Stone, the Asgardian's couldn't restore the Bifrost Bridge.
Steve whispering Hail HYDRA to all those HYDRA operatives in the elevator would cause a massive change to the timeline because HYDRA would be under the impression Steve is working for them, therefore changing the events of CA: TWS, such as the elevator fight scene. Battling his past self would've also been a massive change if it weren't for the fact Steve's past self wasn't under the impression that present Steve was Loki, and due to having his memory altered by the Mind Stone.
Due to Natasha sacrificing herself to gain the Soul Stone, how would the stone be returned once it's been claimed? Therefore this would erase Gamora's sacrifice from the timeline.
Nebula should not have been able to kill her past self because it's more or less the Grandfather Paradox. However she's a cyborg, so her body could no doubt be repaired.
As I mentioned before due to Stark erasing the 2014 version's of Thanos and the Black Order, everything involving Thanos and the Black Order from 2014 onwards should be erased from existence.
Again as I mentioned before, Steve remaining in the past should've erased the events of Agent Carter, plus the events involving Peggy Carter throughout various films. If the Avengers required Steve's help in the future this would be more or less like creating a Marvel version of the british sitcom Goodnight Sweetheart.
Whatever tragedy you think you've just averted time will find a way to replace it, and trust me Barry, the next one... is gonna be much worse - Harrison Wells/Eobard Thawne.
Time is like cement it takes time to set - Rip Hunter.
Whenever you alter the past those changes affect the present and get compunded in the future - Barry Allen 2056.
TBQH after Tony snapped his fingers erasing Thanos and the Black Order, we should've been taken back to the start of Infinity War except this time it's not the Q-Ship hovering above New York, it's the Statesmen carrying the Asgardians, and the Sakaaran rebels therefore a new timeline has been set like cement. With the threat of Thanos averted, time can replace it with something greater in the future.
Edit #1: Extra information.