I've been playing through the game exclusively with the same group of 3 friends. This is largely the case with them as well; everyone's first impressions and first completions have been with this same group of 4.
Last month, my 3 friends got the "Mutual Insurance" achievement (killing a Tank without anyone on the team taking damage), but I did not. Two of them damaged the Tank (as well as me), while one of them did not, yet I was the only one to not receive the achievement. In the Player.log files of both the host and I, all mentions of the achievement read the same: "<b>Achievement_KillTankTakeNoDamage</b> :: Reset".
More recently, we 100%'d R6, and the 3 of them received the "R6 Absolute" and "Destination" achievements upon the completion of R6CX, while I received neither. During the playthrough of R6, our progress on the collection of story logs also desynced. The 3 of them had synchronized achievements, while mine were slightly delayed. Interestingly, due to issues with "Waiting for Master" tonight, I attempted to host the session to see what our experience would be, and doing so gave me the "R6 Absolute" and "Destination" achievements.
When I asked in #gtfo-related-questions, I was advised to reset my game after each expedition, and also make a thread here.