We can agree to disagree then.
This time around the player gets to decide who/what they consider to be the antagonist. Where in previous Bethesda games the antagonist was pre-determined.
With your reasoning you could even argue that it should be hypothetically possible for any game with an antagonist to get a peaceful solution. If you were hypothetically able to join the antagonist's side.
As for the four factions involved here:
- It would take an impossible amount of work for the player to permanently and unquestionably change the Institute (the people in it) to be an organisation that's not a co-existential threat to anyone outside it. They are too pragmatic to undoubtedly adhere to some moralism or ideology. They set goals and anything goes to further those goals.
- It would take a lot of work for the player to permanently and unquestionably change the BoS. For them to accept the existence of Synths, and for them to not consider the mere co-existence of the Institute as a threat, everything they stand for needs to be overthrown. Their codex, and their deepest traditions and beliefs. Besides that, as with the institute to a certain degree, the BoS cares mainly about the furthermore of it's own goals. There's enough material there to warrant a whole new game if the BoS were ever to take the path you propose them to take.
- The Railroad's main cares are the freedom of Synths and the right of Synths to co-exist. There is decades of bad blood, even vendetta, with the people of the Institute and everything it (can) stand for. For them to suddenly trust the Institute, because of one somewhat shady vault dweller, is a massive leap. With regards to the BoS, as long as the BoS is what it is, if the Institute were no longer a factor against their freedom, they would be in conflict with the BoS because they consider them abominations with no rights to existence.
- The Minutemen are no real pre-determined threat to any of the above, although that's only valid for as long as the player character stays alive, and it depends on what the player intends them to be.
So no, I disagree. These factions are blueprint antagonists for each other. These are not factions that will adhere to some political solution to co-exist. I stand by my opinion that peace between them would be a weak-sauce solution.