The layers where this error is occurring must be a part of a Relationship Class.
In ArcGIS, this is a join between two feature classes or tables that is being maintained by the Geodatabase. It can be either a one to one, one to many or many to many relationship. It is based on Primary and Foreign key fields, which contain unique identifiers to link the tables together. Since the Relationship Class is a type of object maintained by the geodatabase, the Key fields are properties of this class and are likely going to be protected from deletion.
What you will need to do to solve this problem is make a list of those feature classes where an error is being raised, and find the relationship class or classes associated with them. You will have to delete those relationship classes in order for the lock to be removed from the particular field in the feature class.
