A change was made to how column permissions work in Identity Manager 8.0.2 as part of the fix for defect 30052. The Release Notes described the change:
"NOTE: By solving this issue, you may now find that objects are not inserted properly because columns permissions are missing on compulsory fields. Table permissions of the respective permissions group are taken into account during calculation of each column permission. Table permissions of different permissions groups are no longer transferred to all columns. This means, a column cannot be edited when an object is inserted if the table permission Insertable is not defined for the permissions group that grants the column permission Editable."
The Insert permission must be manually added to the Permissions Groups which allow users to see and modify the custom columns. The Insert permission must be added to both the base table (ex. Person) and the specific column(s).