Yes, this has been an issue that keeps coming up. I am very glad for your sake that you noticed it before someone took advantage and cleaned out your FC (because if someone has permission to access the chest and the FC gil, you are very unlikely to get anything back).

Keeping promotions to Master Rank only is the safest option, everything else leaves you somewhat open to abuse.
Whlie you are at it, check who is allowed to buy/relinquish the FC house and the workshop (if you have one).
If your FC has a house, players can apply by clicking the placard outside. Ofc, some areas are story-locked which is a problem for new/low level players, they'll be able to access the FC house after they are members but they can't access the housing area to apply