I recently received a task to rescue one of my Abernathy Farm settlers from raiders at the Federal Ration Stockpile. After taking my time and clearing it out, I came to learn that the security doors that hold the community member, on both sides of the room, simply won't open for me. Both terminals that control the doors just say that the doors are busy, rather than actually completing the process and opening them. I looked it up before posting here, and it seems nobody else has had this issue. I even tried using console commands on the security doors. Using the activate command does nothing, while disable/enable work. But I would really rather not have to open up the console every time I revisit the location, so it's just not worth it. Guess I'll just load a previous save and pay off the ransom, and hope future kidnappings don't happen in the same location. Well that, and I also hope that a future update will squash this bug with the fury of a thousand suns.

I haven't had a kidnapping quest yet, but I have had bugged synth/infiltrator quests. I know where the Federal Ration Stockpile is though, I cleared it out earlier on my own without a quest. I entered through a tunnel from the old church directly to the north of the Stockpile. Went through the tunnels and came up inside a building with a terminal. I'm not sure exactly where the doors are that you describe, even though I cleared the entire area. I only mention this because if you haven't gone through those tunnels from the church yet, it might provide an option.

I've explored the entirety of the Federal Ration Stockpile, and the alternate church entrance, so I didn't miss anything. The doors/terminals that refuse to work for me are the ones tied to the maglock doors not far from the main entrance into the stockpile bunker (double-wide maglock doors that can only be opened with master hacking skills, or the password to the terminals that you get off of the raider boss in the back of the tunnels).

Target the door in the debug console and type unlock.

I did, but that didn't do anything for me. Don't recall if I tried doing that first then activating the opening sequence from one of the terminals...will try that next time I'm there, unless the doors miraculously cooperate, lol.

Federal Ration Stockpile kidnap victim is always just through the main door, out in the open on the floor in my game. Not behind any security doors.