I'm attacking the Railroad with the BoS and they're telling me to use a detonation pack. The only problem is that it isn't on the wall. I have no way inside to kill their leaders.

Through North Church perchance?

The back entrance may be available as well, if you opened that up too.

Damn, I wish I'd thought of that.

The bug is because Doctor Carrington is supposed to be outside of the Railroad HQ.

The detonation occurs after his death.

I had to reload before I accepted the quest and kill everyone there.

If you fast travel away and then back again, Carrington should appear in the church. This worked for me on PS4, and supposedly works on the XBox as well.