The first season of the adventurers league, Tyranny of Dragons, seems to be set in DR1489, according to the PDF, "State of Phlan During Tyranny of Dragons". Part 2 of the main adventure for that season, "Rise of Tiamat", ends with Tiamat almost certainly being unleashed on the material plane. That's a fairly important change.
"State of Mulmaster" does not specify a current date for the second season, "Elemental Evil". Furthermore, the likely ending of the previous season's expeditions and "Rise of Tiamat" may be entirely incompatible with this season. The events of each are entirely ignored, despite having serious consequences for all following events. As such, they may be alternate histories set in roughly the same "modern" period, or it may be set somewhat prior to season 1, as "Princes of the Apocalypse" is more likely to have a happy ending with all loose ends nicely tied up.
The third season, Rage of Demons, takes place in the underdark for the most part. The latest date provided in "State of Hillsfar" is DR1487, so it's almost certainly happening in the same time frame as Tyranny of Dragons. "Princes of the Apocalypse" describes a major event in which multiple major Demons manifest in the underdark and attempt to basically invade the material plane. Also fairly significant.
Beyond this point, we are no longer exploring faerun, as the current season is set in Ravenloft, which is a different setting.