Effect: Animals do not willingly approach within 30 feet of you, unless you or the animal’s master succeeds at a DC 20 Handle Animal, Ride, or wild empathy check. Animal companions, familiars, and mounts granted by your class abilities are immune to this effect.
Item 3 isn't quite right--it only applies to animal companions, familiars, and mounts granted by class abilities.
Regardless, if commanded by its creator, a simulacrum will approach a creature Warded Against Nature, as "willingly" doesn't matter due to "absolute command". No check required. If not commanded, the simulacrum will not approach such a creature.
For example: if you order your simulacrum to head down the road to the drug store and pick up some beef jerky, it will swerve out of the way to avoid a passerby if that passerby is Warded Against Nature. If ordered to do so as quickly/directly as possible, however, it will not swerve.
A simulacrum operating without orders, sure. Even one with orders that have nothing to do with the warded creature. It will act as the creature it believes it is.
But the "absolute command" of one guided or under orders from their creator should be treated as automatically having made the Handle Animal check, even if the master is not present. This does not preclude an ordered simulacrum from having to make saving throws to avoid the effects of an aura or spell that calls for a save, so a Repulsion or Anti-life spell would work normally, despite the absolute command of the master. But in this case, when a handle animal check will defeat the ward, it seems absolute command applies.