Gfyuki

(The whole question is pretty much spoilers)

Time travel is a key plot device in Endgame. A central point is that they have to be very careful with time travel, as explained by some team members when Rhodes asked why can't they simply go back in time and kill baby Thanos. Someone mentions that "all the rules apply, no interaction with our past selves, no trying to change the future, etc...". When Hulk meets the Ancient One, she explains that timelines and realities can be damaged, etc...
The only thing they can really pull off without messing up history is retrieving the infinity stones, using them in the present, and then returning them to the proper place in history to avoid any disruptions to the time line.
But then in the final scene, we discover that Captain America went back in time and had the life that he always wanted to have with Agent Carter. Doesn't this contradict the above mentioned dangers of time travel? Wouldn't his getting together with Agent Carter at the very least completely alter the history of the S.S.R and S.H.I.E.L.D (if not the entire U.S military) and hence completely mess up the time line??

Not necessarily. Two things to bear in mind:

First, it was revealed that Peggy Carter had been married sometime after World War 2, but her husband was, notably, not named nor was he seen at her funeral, not was it ever mentioned if he was still living or not.

Second, there's really been nothing shown about SHIELD and Carter from the 1950s to the 1990s, aside from brief flashbacks and references.

So, you're looking at a closed loop.

Rogers returns the Infinity Stones but he doesn't go back to right after his disappearance in 1945; he goes back sometime later, after the years shown in the Agent Carter series, because he knows what she was up to during those years and that his being missing is part of the reason she did the things she did, and what she did was important for events later. Then he shows up, say, in 1950 or so. Maybe he tells her the truth, maybe he just tells her he miraculously survived and just made his way back to civilization from the crash, but he wants to get away from the life and retire.

So he assumes a false ID and marries her.

He knows about HYDRA infiltrating SHIELD, but doesn't say anything because he knows events have to play out, and he carefully plays the role of husband not involved with the secret agent life.

Peggy starts developing Alzheimer's and is well into the dementia stage when

his past self, still frozen in ice, is found. At that point, he has to be careful not cross paths with his younger self, so he avoids visiting her when he knows his younger self will be there, sits quietly in the back at her funeral, and then waits to reveal himself to Bucky and Sam after his younger self has made the jump back in time.