I feel like they did a very poor job of explaining that in the movie. They talk about how movies like the Back To The Future trilogy - which does involve time travel creating alternate timelines - always get it wrong, and they make it very clear that the Infinity Stones must be returned back to their original point in time in order to prevent a disruption to the timeline. The whole reason why they bring back the Snapped people five years later instead of just reversing the entire Snap via time travel is to prevent a paradox. And when they first go back to New York, they seem to be doing their utmost not to disrupt existing events so as to avoid rewriting their own past.No, you got it. The thing we need to realize is... Old Cap is not Cap. At least, not "our" Cap.
When you travel in time, you go to alternate timelines. They establish that the way you get back to your own timeline is *through a portal*. Cap and Iron Man even initiate a jump (to 1970) without a portal, but to return, they use the portal. Without the portal, any time jump you make is to an alternate timeline.
Old Cap did not come through the portal. So, it isn't our Cap. He's a Cap from an alternate timeline.
There's actually a ton of timelines going through much the same thing - each with their own Thanos trying to kill off half the people in its universe. There's a bunch of Avengers jumping through a bunch of alternate timelines trying to do much the same thing. But... *we* are an alternate to someone else. So, Our Cap jumps out, goes to an alternate timeline, and spends a life with alternate Peggy Carter. A *different* Cap jumps from somewhere else into our timeline to deliver the shield.
Even when Hulk debates with The Ancient One about how taking the stone will create another, darker timeline, he wins her over partially by demonstrating that its return will prevent that timeline from ever existing.
So, are those alternate timelines still out there? Did they get nipped off when Captain America went back in time to return the stones? Since the things that happened in those timelines are now part of these characters' pasts, how can they be unmade without causing a paradox? If they'd simply gone back in time and prevented the Snap, wouldn't that have created a timeline in which everybody lived, without so much hassle?