Can Baron Nashor be targeted by an enemy Battlefield effect, i.e. Amateur Recital that's controlled by an enemy?

No — an enemy-controlled Amateur Recital cannot target Baron Nashor.

Baron's ability says he can't be chosen by enemy spells and abilities, and a battlefield's ability is controlled by its controller (Rule 190.6.a). Since the enemy controls Amateur Recital, its hold trigger is an enemy ability, and choosing which unit to move to its base counts as "choosing" that unit for targeting purposes — the word "choose" doesn't need to appear on the card. That makes Baron an illegal choice (RiftJudge FAQ #8771; Rules 355.9.b, 355.10).

This is true regardless of which battlefield the units are on — the battlefield's controller, not the battlefield's owner, determines whose ability it is. If you controlled Amateur Recital, you could move your own Baron, since it would be a friendly ability.