A left handed AR can not be used as a "Service Rifle" in NRA matches. Left handed AR's are not standard issue which makes it ineligable for Service Rifle competition. An ambidextrious safety also makes your rifle ineligable for "Service Rifle" matches.
You may have a left handed AR with or with out an amibidextrious safety and shoot it in the "Match Rifle" class though. Nothing wrong with that.
As a fellow left handed shooter I have no problems shooting with "right handed" AR's. And I also shoot competition and have not noticed my performace hampered shooting a right handed AR.
If your looking to shoot "SERVICE RIFLE" it has to be a standard issued rifle on the outward apperance but the trigger/hammer, barrel, bolt/bolt carrier, and sights can be custom. They just made the A4 20" an acceptable rifle for Service Rifle competition because the military has started to issue that configuration as a standard rifle.