The document Renown Benefits v1.01 states:
Characters are free to join a faction as their membership allows. While most have no special requirements, some do (for example, members of Bregan D'aerthe must be drow). A character may only be a member of a single faction at any time, and earning and maintaining membership in a faction requires a character to use the background feature 'Safe Haven' (from the Faction Agent background, as found in The Sword Coast Adventurer's Guide).
Characters can leave their faction at any time. To do so, they simply remove the Safe Haven background feature and replace it [with] the background feature they had prior to joining the faction, then set their renown to 0. If the character did not have a previous background feature, they may assign one; once assigned, this feature is subject to the standard character rebuilding rules.
May a faction may be joined at any time, even at level 5+? Or does joining a faction fall under character rebuilding, which, per the Forgotten Realms Adventurers League Player's Guide v8.2, cannot be done after reaching level 5, except for "other, non-mechanical aspects of your character"?
You may choose to rebuild your character prior to playing their first adventure as a 5th-level character (levels 1–4). You can change any of your character's statistics but their name. Other, non-mechanical aspects of your character such as their alignment, sex, gender, or personality traits can be changed between sessions regardless of their level.
Your character keeps any rewards and equipment earned to that point. If you change your characters class or background, they lose any equipment (along with the proceeds from selling it, or benefits derived from it, such as copied spells) associated with the class or background. Similarly, if you change their faction, you also lose any renown from their former faction.
Does joining a faction fall under "other, non-mechanical aspects of your character"?