There is a way to get around this partially, which is that they don't change the access codes very much.It appears that this is a bit more challenging of a task than your average PP2 assignment.
As has been mentioned, apparently you need to either clone someone's access rights, or have an e-breach device, in order to open those containers.
So:
- go to the base, find a terminal that's either well out of the way or can be easily escaped from (there's often one at the landing pad itself, for example)
- e-breach the terminal which won't take long, use that to get the approximate location of the containers, write down or memorise the codes
- leave the base, go to supercruise, return to the base (there's now no e-breach that someone might find)
- open the containers with the codes you wrote down earlier, without needing to have any clearance right now
- ...though picking up the Powerplay items within will count as stolen goods, so you'll be wanting to get back to your ship very promptly at that point!
Or you can find offline bases and get them that way: if it hasn't told you a specific system this is much simpler and you can pick up a bunch of side merits from the reactivation missions, etc. That's what I did last week and got quite a lot of merits in total from all the Powerplay loot, the reactivation missions themselves, and uploading malware on the side.