The Release States will be applied to content during the different stages of the translation job life-cycle.
The Localize users need sufficient permissions to view and work with the content they'll be editing.
A minimum of list, read, modify, change into state, change out of state permissions must be set for the Release States for import and export of the translation jobs.
For the states selected in 'Only send source objects in these release states for translation:' the minimum is list and read.
For more information on how Release States are used by the Localize module, see: Release States Screen.
For more information on the Localizer role permissions, see: Setting Role and Folder Permissions for the Localizer Role.