I read somewhere else you can build an elevated platform (using the shack foundations) that can only be reached by jumping, which apparently works because settlers can't jump. My current solution is to build a fence around my armour, and when I want to access it I go into Workshop Mode, click on a piece of fence as if to move it, walk forward through the gap, then cancel, so the piece of fence goes back where it was. After I got stung by this and got my armour back I went round all 20 settlers at Sanctuary Hills and found a second settler who was walking around with a fusion core in their pocket (as well as the first one who got in the armour and I pickpocketed the core back from). So far the comments and answer are concentrating on the 'settlers take things from containers' part of the question, but I'm also trying to ensure a settler won't get in power armour if they have a fusion core already. What is the best way to prevent settlers taking your 'personal' gear, and how do you prevent settlers from taking power armour if they have their own fusion cores? I eventually pickpocketed the fusion core back (which took lots of reloading because I only had a 7% chance to succeed) but I don't want to have to do that again. The thief wouldn't get out of his armour. Usually I trade with new settlers to take nice loot from them and make sure they have some ammo and a bit of leather armour, but I must have not done that for this guy.ДЄpparently you can get NPCs out of armour by talking to them, but after the mutant attack everyone just said 'thanks for the help, pal' and 'you arrived just in the nick of time' (over and over and over, if I hear it once more I'm going to feed them to the next super mutant attackers). But when the mutants attacked one of the settlers still stole a suit of power armour! I think the settler must have brought a fusion core with them when they arrived in Sanctuary Hills. I loaded an earlier save and when I arrived in Sanctuary Hills the first thing I did was take all the ammo and cores from that cabinet, to stop anyone stealing them. Apparently that isn't safe, because Marcy helped herself to that cabinet! I think they can also take things from the workshop, so I stored all my good stuff in a cabinet next to the power armour repair frame. The strategy guide says settlers will only take things left out in the open: Before I knew it Marcy Long had taken a Fatman and all my mini-nukes from the cabinet where I store them and wasted three mini-nukes on mutant hounds, and another settler had stolen one of my power armour suits and 21 fusion cores! After clearing out a location I travelled back to Sanctuary Hills, where I keep all my spare power armour and my fancy weapons, and it was under attack from super mutants.

Fallout 4 steal power armor