Anyone giving me a quest should attempt to weasel out of it, set up assassin contracts on me instead of paying, or simply run away without paying when I report in for clearing quest. Rationally, considering the factions are at WAR, in other faction territory I should be identified as a spy, have wanted posters with my face on them, and be killed on sight by any guards or military personnel.
Running around PVE, once I moved beyond my own faction territories (to clear shards and pick up up lore books), it became clear that in the other faction areas government officials and others are happy to offer me quests, even quests against my own faction.