Ok the Railroad are a group dedicated to protecting synths, so why in all their experience and wisdom do they commit one fatal action that will inevitably wipe them out? The Institute is the only "known" place in the world that can create synths. Synths in turn can not have children. So their only means to reproduce is destroyed by their would be saviours!
The Brotherhood of Steel are a group dedicated to the preservation of advanced technology. The Institute is full of advanced tech. They blow it up! Now I know what your thinking that they wanted to destroy all traces of the synths, heck it is mentioned by the scribe in the game, but the Institute was more than just synth building, it was full of tech, a nuclear reactor, Bioengineering, FEV research, and teliporters!. They could have easily killed the scientists and destroyed all traces of the synths. Then they would have a great base for when the airship leaves, teleporters and everything else mentioned.
The MM these guys are dedicated to protecting civilians, so they destroy an underground bunker filled with food, living quarters, and a nuclear reactor.
The Institute is run by someone who for the most part is insane so I guess he can be forgiven for making odd decisions.
Back to the RR for a second, I did the airship level twice once by stealth and second by killing everything that can be killed on board. Now If I can kill the BoS why not take the airship! It'd be easy to get all the synths out of the Wealth in a huge armoured airship.