A new feature to restrict import/export of specific entity types based on admin user roles was introduced to the module in version 1.7.0. The functionality is available as a part of an active product subscription or support subscription. You can find the 'amasty/module-rolepermissions-subscription-functionality' package for installing in composer suggest.
This functionality applies to default Magento import and export only.
This can be configured in Advanced: Import and Advanced: Export tabs on the Role edit page:
— Advanced: Import
— Advanced: Export
As an example, this user can only import 2 entities: