This article provides information on why legitimate emails from external users may suddenly be getting blocked after turning on Spam Blacklist function.
This is mostly affected by which Blacklists are in use and the reputation of the servers from which emails are received. Most likely, the sender(s) are blacklisted somewhere.
If this always happens with the same senders, whitelisting their IP addresses should resolve this. Otherwise, they will need to tinker with the settings and find out what works best for them.
If disabling all Blacklist checking is not an option, they can either disable individual Blacklists that cause the most trouble or alter the way it behaves (e.g. Whitelist the sender's IP, set the list where the sender is listed to add score rather than block).
Please check the article on Spam Blacklist function is blocking legitimate emails from external users for more options.