So, Avengers: Infinity War is him getting the Infinity Stones, causing the Blip, and then destroying said stones. Avengers: Endgame is the Avengers undoing the Blip, and then Snapping Thanos (and his army) away. This means that the pre-Infinity War Thanos is Snapped, thus meaning that he doesn’t exist for Infinity War. Then the Grandfather Effect happens.
Can someone explain why Snapping Thanos doesn’t break time/reality?
The Hulk explains clearly that altering the past doesn't change the future from which the time traveler originates. Instead, it creates another branch timeline/reality in the multiverse (or time follows a different potential path within the multiverse - basically the same thing).
When the Avengers arrive in 2014 via time travel, they create a new timeline/reality, and it is the Thanos from that branched timeline that use the quantum realm to jump back to the time and place from which the Avengers time traveled - the original timeline/reality.
This also means that they create new timelines/realities in 1970, 2012, 2013 (whenever Thor 2 took place), and 2014.
Even though it's not technically canon (yet), this concept is furthered in Season 7 of Agents of SHIELD when they use the quantum realm and a separate timeline/reality to hide from the Chronicoms, and end up back in the original reality as they left it even though they completely changed the events of the timeline/reality where they were hiding.
I tend to think of time travel/multiple realities like a graph, such as a git repository where you can branch at any point in the history of the project, create a new branch, merge it with the main branch, rebase it and change its history, etc.
When you alter the past in the MCU, the past you knew doesn't cease to exist. Rather, you create a branching timeline forking away from the previous one, so you now have two timelines where you previously had one. This isn't directly stated in the film, but it is indicated by the following conversation between Bruce Banner and the Ancient One, and a branching timeline diagram conjured by the latter.
THE ANCIENT ONE: I'm sorry, I can't help you, Bruce. If I give up the Time Stone to help your Reality, I'm dooming my own.
BRUCE BANNER: With all due respect, I'm not sure the science really supports that.
THE ANCIENT ONE: The Infinity Stones create what you experience as the flow of time. Remove one stone and that flow splits. Now, this may benefit your reality, but my new one... not so much. In this new branched Reality, without our chief weapon against the forces of darkness, our world will be overrun.** Millions will suffer. So, tell me, Doctor, can your science prevent all that?
BRUCE BANNER: No, but we can erase it. Because once we are done with the stones, we can return each one to its own timeline at the moment it was taken. So, chronologically, in that reality, it never left.
Avengers: Endgame
So when the Avengers went back in time to borrow the Infinity Stones, they created a series of alternate timelines where the Snap never happened, because the Stones weren't present in these alternate timelines in 2018. Each of these alternate timelines had its own version of Thanos, and it was one of the alternate versions of Thanos who travelled forward from 2014 to 2023 and died there in the film.
The events of Avengers: Infinity War, including the Snap, still happened, but they happened in a timeline which was now running in parallel to all these other timelines. A parallel universe, in effect. And when Captain America returned the borrowed Infinity Stones to the times and places they were taken from at the end of Avengers: Endgame, this erased the alternate timelines that were created by the Stones being borrowed in the first place (as per the Ancient One's branching timeline diagram in the video clip above), leaving only the timeline where the Snap occurred.
