Only presuming a Back to the Future style time travel set-up, which they obliterated as their version of time travel anyway. In the MCU, time travel doesn't result in changes to the past--it creates another reality. So, for example, by going back to the '70s, both Captain America and Tony Stark created an alternate version of that time period. It's pretty small in difference from the base MCU, all things considered. However, there are enough changes where it will change a few things about the universe. The same is especially true with what they did with Loki and the aftermath of The Avengers. Loki's getaway wasn't supposed to happen, Cap getting the scepter certainly wasn't supposed to occur either, the Ancient One and Banner weren't supposed to have their conversation, and past Cap and future Cap were never supposed to fight. This is a rather large change to this alternate reality--one that will probably have relatively devastating consequences for it. However, it is impossible to know for sure.
The biggest change is, of course, what you mentioned. When Old Nebula brought Thanos into the future, it only solidified that this alternate universe Thanos was now totally different from the previous universe's. That's why killing Old Nebula didn't kill New Nebula. She had become an alternate reality version of herself the second New Nebula stepped back in time. The same is true with Thanos--it doesn't undo what the original prime Thanos did. However, it does stop Thanos from being able to execute his plan in the alternate reality that was created by their time jump. So, Tony Stark wiping out Thanos and his army not only saves his 2023 universe--it saves the new universe that still is set in the year 2014.
I know a lot of people have been pointing out issues with this timeline stuff though. Some people have had the question about how Captain America went back to these other realities. Well, time is all relative. So, while days have passed since their insertion in these realities, my guess is that they can place Cap directly after the time that they "synced up" in that new universe and continue to alter the events of that universe (this time by replacing the stones where they go). This new reality that has already been created, thus, will not further branch off. As Hulk said, they can replace them as they left. Cap will go back in time to all these places and replace the stones in these realities so that no alternate reality exists without the stones where they should be.
The biggest question mark then is how did Captain America come back as old Cap? Well, the simplest answer seems to be the most logical one: Steve went back in time, created an alternative reality, and moved forward in time as usual. In this universe, there are two Caps. One does eventually get unfrozen (when that is is hard to say). One is able to just reunite with Peggy immediately. He's able to have his life. Of course, we know that he also has the ability to perform his duties as Captain America--which means that he would probably further affect the timeline by saving Bucky in this universe from years of torment. I would actually anticipate that some of these changes, while positive in the short term, could yield consequences dangerous for the universe in the long run. All this time meddling and creating alternative realities, I'm guessing will lead to Kang the Conqueror coming from one of the futures of these realities to the prime MCU, where his counterpart never dealt with these consequences.