How do you stop anyone taking stock from the alliance store without permission?

You cannot stop people buying items from the alliance store if they are in your alliance. No one else will have access though.

The only option to stop purchases is to not stock it. Only the leaders R4/5 can add items to the store, and if there is no stock then it cannot be bought.

There is no reason not to let your alliance members buy items though. They will have to donate to the alliance Tech to earn the points first and you want them to donate to make the alliance stronger.