You haven’t shown an example of the problem, but the usual cause is trying to set global privacy (using Admin > your family tree > privacy screen) on a note stored at a low level, or subsidiary to some other tag.
That is not possible via the global privacy screen. It is only usable for ‘level 1’ records. The same limitation is true for media, sources etc.
So, if you add a note to a person, the setting will work. But if you add a note to the birth of a person it will not. You would need to add a privacy ‘restriction’ to the birth.