TL;DR
Logistics bots should actively try to fix filtered Storage Chest contents when a filter is in place.What ?
When a Storage Chest is first placed, it has no Logistic Filter and anything can be placed there.If a filter is later applied, the chest may already contain items that are not whitelisted.
Logistics Bots should try to remove the blacklisted items from the Storage Chest as if it were an Active Provider Chest for those items.