Does the Axis matter for the consideration of “Sharing an alignment component”?

Specifically in regards to the Insinuator archetype for the Antipaladin, my question is really about their variant Smite Impudence feature.

It states:

Smite Impudence (Su):

Once per day, an insinuator can beseech the forces empowering him to punish their shared enemies. As a swift action, the insinuator chooses one target within sight to smite.

An insinuator cannot use smite against a target that shares an alignment with the outsider he has invoked for the day.

And then goes on to describe functionality exactly as any other smite (+Cha to hit, +lvl to damage, etc.)

Essentially, at the start of each day, you pick an outsider that has an alignment within one step of yours, and then can Smite targets that have alignments that oppose it, ie LE can smite CG, CN, NG, and TN, but not LG, LN, LE, NE, or CE.

My question is, on the dual alignment axis of Good Vs Evil and Chaos Vs Law, how does Neutral apply? Specifically, does a LN creature have protection from an NE smite? They are both Neutral, but from a different Axis. Does the Axis matter for the consideration of the alignment component, or is simply being Neutral on either axis enough to thwart the Smite?