Blind Betrayal

Blind Betrayal is a Brotherhood of Steel main quest and achievement/trophy in Fallout 4.

Background
As the Brotherhood of Steel finds itself on the verge of success in their Commonwealth invasion, a startling discovery is made of one of their own. A paladin that was considered one of their best, has a secret, and now a hard decision needs to made for their future.

Detailed walkthrough
After Liberty Reprimed is completed, the Sole Survivor is ordered to report to the Prydwen. There, a furious Elder Maxson confronts the Sole Survivor, demanding to know if they were aware Paladin Danse was a synth. He reveals that the network hack of the Institute's mainframe yielded indisputable proof Danse is not human, but is actually a missing synth unit with the designation M7-97. The Sole Survivor is then given a choice of medium-difficulty persuasion checks to convince Maxson they did not know Danse's true nature. Alternatively they can suggest that Danse himself may not have known he was a synth.

The Sole Survivor is then ordered to find Danse, who has gone AWOL, and execute him. They meet with Proctor Quinlan to figure out a way to track Danse down, but their deliberations are interrupted by Scribe Haylen. Haylen pulls the Survivor aside and makes a plea for mercy on Danse's behalf, desperate to save him even if he is a synth. She then directs the Sole Survivor to the recon team's previously declared fallback location: Listening Post Bravo.

After dispatching the security measures (two exterior turrets, one exterior Protectron, and three additional Protectrons down the elevator), the Sole Survivor will locate Danse inside the bunker. There they must decide how to proceed.

Plan A: Carry Out the Execution
The Survivor may execute Danse with or without speaking to him. Alternatively one can let him commit suicide. On his body they will find a synth component and Danse's holotags. Collect the tags, return to the Prydwen, and inform Elder Maxson the deed is done.

If the Sole Survivor enters the bunker and is seen by Danse, then leaves the bunker, Danse will commit suicide.

Plan B: Allow Danse to Live
The Sole Survivor may refuse to execute Danse. He will protest, stating synths are abominations and that he must be made an example of. Passing a medium-level persuasion check will convince him he is no threat to humanity and should flee the Commonwealth. Danse hands over his holotags to appease Maxson, then asks the Sole Survivor to meet him on the surface to say their farewells.

Outside the bunker Danse and the Sole Survivor are met with an unwelcome surprise: Elder Maxson, having suspected the Sole Survivor would prove insubordinate, has followed them to the bunker. Outraged, he reiterates his orders and demands the synth's death. From here the Survivor has three options:
 * Concede to Maxson and kill Danse. Danse will submit peacefully.
 * Fail to convince Maxson to spare Danse OR request he perform the execution himself. Maxson will kill Danse.
 * Persuade Maxson to let Danse live. Maxson will reluctantly agree, but will exile Danse from the Brotherhood. As a known synth Danse will be fired upon by Brotherhood soldiers.

Whatever decision is made, return to the Prydwen. Maxson will promote the Sole Survivor to the rank of paladin in addition to granting them all of Paladin Danse's belongings, including his living quarters (the room marked "Prydwen Quarters" which is locked before this quest) and his personal set of T-60 Power Armor.

Bugs

 * Once Elder Maxson arrives in the Vertibird after exiting the listening post, he starts walking off into the distance making it very difficult to enter dialogue with him. One potential fix is to continually step in front of him and prevent him from moving too far away from Danse, allowing Danse to be spared or executed by Maxson. If he does get away, the quest can be completed by executing Danse personally and finding Maxson to the north and briefly talking to him to return him to his quarters. Alternatively, on PC, select Maxson in the console and use the command to take control of him to stop him walking away and complete the dialogue. Use the  command again to return him back to AI control. You may need to use  to return control to the player character if one uses this method. Another method is to use  to forcibly set Maxson directly in front of the player character. If one stands close to Danse, Maxson will be hemmed in between, and the scene will play out to the end.
 * If the Defend the Castle quest is in progress, pending an attack from the Institute, you can still complete this quest but there can be some bugs. First, the quest marker will be tracking Danse as opposed to directing the player character to Listening Post Bravo. However, console commands (PRID for Danse and then moveto.player) can be used to summon Danse to the bunker at Listening Post Bravo. One will need to summon him again upon coming up again before the final confrontation with Maxson. When Maxson speaks to the player character, Danse will start running in what looks like the direction of Sanctuary. Unfortunately, this can easily trigger Maxson to give up on the conversation and 'execute' Danse (he moves forward and makes an execution motion where Danse should be standing). The only way found to fix this is to rapidly click through dialogue. Upon completion, one must talk with Danse before returning to Defend the Castle, otherwise the request will fail. This is difficult because Danse is running away, and the console command to bring him to the player character no longer works. A tracking mod can be used to catch up with Danse, or alternatively one could try manually heading east in the hopes of catching up to him at Sanctuary. One can complete the quest by talking to him and if the player character invite him to stay with them, he will show up at whichever settlement he was last sent to.
 * If the Institute is destroyed by the Minutemen, Elder Maxson will say he is busy and will refuse to speak to the player character, therefore he cannot give the quest. Also in the police station, Scribe Haylen's dialogue will suggest one has completed the quest even if this is not the case. Danse will remain in any settlement the player character has left him in and he will continue his normal dialogue and will stay in his power armor.
 * Upon exiting Listening Post Bravo with Danse (having refused to kill him), the dialogue in which one has the option to either execute Danse or persuade Elder Maxson to let him live may be skipped altogether, resulting in the immediate execution of Danse by Maxson.
 * If one already has a set of power armor on the rack Danse's suit defaults to, his will not appear (although the inventory screen will flicker upon looking at it). However, if the player character enters the suit they will enter Danse's - leaving the old one behind.
 * If Paladin Danse was one's companion when starting Blind Betrayal, he may still be invincible upon encountering him in the bunker. One potential fix is to convince him to live, then hand the execution order to Elder Maxson, which will result in the quest progressing.
 * Upon arrival at the bunker, Danse may be wearing no clothes, which may be due to upgrading Danse's power armor. Any upgraded components will not be available on the suit of power armor retrieved from the bay in the Prydwen.
 * This can also occur if Danse's BOS Uniform was unequipped while trading gear with him. The uniform cannot be re-equipped after removing, resulting in Danse wearing just his underwear under his power armor and, thus, just underwear during Blind Betrayal.
 * If Elder Maxson is killed after the interaction with Paladin Danse and before he enters the Vertibird, Elder Maxson will appear dead upon exiting the Prydwen during Rocket's Red Glare. Using this method it is possible to duplicate his battlecoat.
 * If Danse is assigned to a trade route prior to relocating to Listening Post Bravo, then whichever trade route he was provisioning will remain permanently active for the rest of the game. If Danse is then spared he can be assigned to another route and both will remain active.