Honestly, it sounds like something got lost in translation in this choice--it's pretty boilerplate for quests in these kinds of games to (a) not really "count" until you've actually started or finished them (let's be real, a common playstyle is "collecting" all of the quests in the area and then deciding which stories seem fun to tackle at that moment); and nevertheless (b) commonly involve a double-crossing or Come-to-Jesus aspect (e.g., someone tells you to kill person A, and you go and tell them, resulting in a chance to get back at the would-be-assassin mastermind). Much like sparklecat above it didn't at all dawn on me that merely accepting the Dozens' quest (in a mechanical way) would get me locked out of all the other questlines... and through the rich lore and content I encountered through the other game quests, "my" perspective on which faction I would want to join changed. Also, how on Earth do the other factions magically know I decided to embark on a secret mission for the Dozens that I haven't actually enacted as of yet? I don't even think I've done anything for the Dozens other than chat someone into giving up some armor! (I even killed some of their agents on a different quest!)... To me, locking out at that stage doesn't even make sense from an in-universe perspective, nevermind a game-mechanics perspective.
I'm about to dive into the woolly world of altering the game flags manually to reverse the "choice," because it's been probably 15+ hours since I accepted the Dozens' quest way back when. It feels really disappointing--given how fun and reactive the rest of the game is--to not be able to "play out" my character's story due to a somewhat opaque and artificial lock-out. I think it would be fair just to reset that quest threshold for folks who clearly have not done anything beyond accepting the quest, or change the flags to be lockout for completing the quest (either to a certain meaningful point or in total) rather than provisionally accepting it