It is now possible for all shippers based in Northern Ireland to ship to Republic of Ireland using any International service. All other shippers are still required to not submit any parcels for export.
Currently allowed services for all UK based shippers include only RM International Business Standard and RM International Business Economy (untracked) personal correspondence items (Letters and Large Letters).
Further information: https://personal.help.royalmail.com/app/answers/detail/a_id/5317/