This quest is a unique and brief transitional event where you essentially render The Railroad irrelevant. Its reliance on its Institute mole becomes its undoing — if you alienate yourself from The Institute during Underground Undercover. It's significant because by banishing yourself from The Institute, The Railroad loses its only method of contact with the mole.
To reiterate: This quest can only be triggered during Underground Undercover and will block you from all future Railroad quests.
What is the easiest way to get on The Institute's bad side? Kill Father. This event will also trigger the Banished from the Institute quest, which requires that you escape from The Institute. Note that you cannot use fast travel.
If you manage to escape, report to Desdemona. She'll express a surprising sense of defeat, now that the Railroad's only inside source is blocked off. Underground Undercover will be classified as Failed, and she will advise you to continue the fight by aligning yourself full time with The Minutemen. Speak to Preston Garvey to complete the quest. You'll find him at Sanctuary Hills.