The Institute, objectively, needs to be destroyed. They treat surface-dwellers like radroaches and willingly destroy them for the sake of humanity - redefined to mean only the Institute. Desdemona actually goes out of her way to announce that they will rescue every Institute personnel that they can, before I could even bring up the idea of evacuating them. They aren't heartless brutes sacrificing human lives for synths, otherwise they would not be actively rescuing the enemy While destroying their base. Punitive Institute activity? They're already destroying lives.
Destruction of the Prydwen, see above, is a direct result of the Brotherhood making targets of the Railroad sending Paladins to raid their hideout after the Railroad conducted 0 anti-Brotherhood activities. When a giant military force knows where you live and made an attempt to preemptively destroy you, and you've run out of hiding spots already, you do something about it. Regretful that the Brotherhood's child soldiers went down too, but child soldiers are just part of the wasteland.
As far as rescued synths going Raider: so what? Only example we have is one synth going bandit, after his stint with the Minutemen ended due to minutemen dissolution. Sounds like a great deal if you ask me, synths being subjected to the same environmental pressures as humans, and making the same decisions. Human or toaster, that's a very human thing to do, and damning synths taking that action would be to damn humanity for doing the same. But that'd just be silly.
Though if Railroad was anything like PETA, they'd be destroying the synths after liberating them to make sure they never have to suffer 