I went through a couple of sources but could not find a solid statement on how exactly Railroad was founded and decided to stand up for the synths. Is there any more or less official info on this?
Taken from Fallout Gamepedia:
The current incarnation has its roots in the remnants of the organization that persisted after an Institute raid that destroyed the faction's headquarters in November 2266. With thirteen survivors, Wyatt held an election and started to rebuild the organization from scratch.
in turn taken from one of the Railroad HQ terminals:
Gathered surviving runners, held an election. I lost, or won, depending on how you look at it. After the HQ massacre, most people simply left the Railroad. Only one person survived HQ, a runner named John D. He called out for volunteers to get some of the old files. No one stepped forward.
My job is to rebuild the Railroad from scratch. I think where Agamemnon went wrong, is that HQ was known by too many people. I'm theorizing here, but once the Institute hit a safehouse and leaned on anyone the HQ would be easy to find. But how could Agamemnon know just how deadly those damned Coursers are?
Current count: 13. 0 synths.
How the hell do we rebuild from here?