I played as the Institute:
Railroad Show stooper - hard to tell, but I believe it's when you are involved in the war at Bunker Hill. The leader will tell you to leave if you try to talk to her after that.
Brotherhood - You get a popup, but it's just before you teleport to the Mass Fusion Building
Minutemen - I think it's when you hand over the stolen Institute data to the guy at your base, and tell him "The Institute isn't the enemy", but I could be wrong on that. They might also be like Yes Man in NV, where you can go with them no matter what (in case you piss off every other faction)