They don't, that's the problem.
The KNIGHTS do ie. if you go to take their 2nd quest. The DOZENS do not, however.
Possible bug?
I find this screen somehow implying that other factions will stop working for me faintly amusing (as some here have stated), and it's largely because of this screen I set the game down and wandered off. That's not reading comprehension or a lack of intelligence, that's not translating a game defining moment into anything resembling a game defining moment.
I did accept this quest, assuming that, like the mass majority of quests in this game that can give positive or negative results, that the following would be true:
A) The damage will be to my reputation, given that I'd be "stepping on toes." Other quests with divergent results to kill me reputation exist, and did so at the end.
B) Such damage would happen when I completed this quest, as is the result with every other quest. That is, you know, logical.
C) Should I need to I could advise other people involved of the quest of what was happening, in this case the Crucible Knights.
D) I could turn around and backstab them by not giving them the goods, or choosing an option which makes them hate me when completing said quest.
Instead, I was confronted by a situation in which, before I had even gotten a chance to speak with the knights in detail about what they wanted to the same degree as the Dozens, who I had finished a quest for (their first one being easily completable, as their headquarters being the first found by most players), I had accepted a quest nine hours in that I learned would massively limit my control of the situation 31 hours in, because this quest was constructed differently from the norm in this game. I hadn't even accepted the first Knights quest yet, but they still let me take it (even though I was now secretly to me but openly to the game world allied with the Dozens), where I learned more about the Knights in particular and their leaders. It endeared me even more to the Knights, since most of the interaction you have prior to that is either via hearsay or the first Dozens quest (and boy do the Crucible Knights not come out looking good). Suddenly I had none of the freedom prior quests gave me. On top of that, there was no mention of a dire circumstance, the knights still let me do quests for them, and I'd already alienated the Doemenels. And I had no problems with the way that turned out, even if I couldn't foresee the consequences of my actions, because it followed a logical moral and storytelling framework. It made logical sense. My boyfriend who is also playing told me he was on their good side and what I missed out on, and I didn't even care; I made a decision based on facts and moral exactitude and it made sense.
But the available information does not logically follow in your decisions regarding the Dozens. I killed their men to help the Knights, and they don't care. That's not assuming a side. But accepting the second quest from the Dozens is? My actions to protect animancy and my commentary in public should be endearing me to the Knights, and not those who hate it, the Dozens.
The problem is that with the way the Dozens are set up, players who are only too happy to help the Knights, who have followed the story, read the lore, and have been doing the quests asked of them, are suddenly told that a decision often made many hours previous with a serious lack of signposting can't be changed. Not if we slaughter every single Dozen we find. Not if I slaughter their little buddies torturing someone in the city (they still want me as an ally when I killed their guys to help the Knights, and that's considered reasonable, but the above screenshot is entirely fine?). Not if I tell them they are horrible people and I hope they die to their face. I don't even get an option to lie in the quest turn in, don't get an option to tell the Knights, nothing.
It's jarring to have the level of freedom I had in the game stripped from me, and it's jarring that there are no solutions available to fix it. It jarred me right out of the storyline so much I actually stopped playing.
What about the defence.
A) Unintended consequences are good! Even when true, illogical ones that disrupt RP and are counter-intuitive typically aren't good when you are constructing a narrative.
B) But it tells you! Maybe for the Knights of Doemenels it might be acceptable, but at the very least the Dozens doesn't make it sound like a game changer. Hardly the "clear warning" advertised above.
C) It doesn't even matter to the story. Other than changing the story, a lack of consequence doesn't make it any less jarring, nor does a further problem in a lack of consequence make the first problem of a lack of knowing of consequences any less relevant.
D) But you can backstab them later. A given, although also weakens the argument people make that you should be able to backstab them before too. I still shouldn't be railroaded into going with a group I don't want to, especially when I'm supposed to be immersed in a storyline. When a criticism of people who made the same error is "learn reading comprehension" (regardless of relevancy) it shouldn't also come with "but also entirely disassociate yourself from the storyline."
At the end of the day, when the argument that things are fine runs along the lines that "you shouldn't care about the story too much" while also demanding "you read better," not only are they contradictory, they kind of run contrast to the flavour of a role playing game. My thoughts anyways.