Jesus Came to Save the Unbelievers?

The answer lies in the broader context of John 12:44-50. Jesus' point is not that he won't ever judge the unbelievers -- after all, in verse 48 he says that his word will judge unbelievers on the last day.

I think John 3:16ff. is probably John's commentary on Jesus' words as we find them in John 12, but even if Jesus was speaking in both texts, there is a different emphases in John 12 than in John 3. In John 3 the focus is on Jesus and the work he came to do (namely saving believers, literally "all the believing ones" rather than "whoever believes"). In John 12, the focus is on the Father. Jesus speaks in extreme and hyperbolic terms in John 12 to emphasize the fact that everything he does is according to the Father's instructions.

For example, in John 12:44 Jesus says, "He who believes in me, does not believe in me but in him who sent me." Strictly speaking, that sentence is self-contradictory: those who believe in Christ do not believe in Christ. But Jesus is simply using a rhetorical device to emphasize the fact that he is doing the Father's business (cf. John 12:49).

The same thing may be true in John 12:47-48 where Jesus says first that he does not judge unbelievers (v. 47a) and second that he does judge unbelievers (v. 48a). Rather than being a contradiction or a severe case of hair-splitting, it may simply be rhetorical device pointing out the fact that the judgment of unbelievers ultimately comes from the Father, even though Christ is the instrument through which judgment is proclaimed and rendered (cf. John 5:22).

Another possibility is that Jesus is referring to different redemptive-historical eras. In John 12:47a, he may well be referring to his first advent, during which he did not come to accomplish the work of judgment but the work of salvation. In v. 48b, however, he is clearly referring to the last day, the day on which he will execute judgment. This intepretation might be paralleled with John 3:16-18 if one takes John 3:16-17 to refer to Christ's first advent, and John 3:18 to refer to his second advent. Although this may sound artificial at first, John 3:18 does speak of condemnation, and we know that the last day is when final condemnation actually takes place. John 3:18 speaks of it as already having been determined, though not yet carried out. Similarly, in John 12:47-48a, the verbs are present tense. But in John 12:48b the verb is future tense.

Another area of difficulty you are encountering is the definition of the word "world," both in John 3 and John 12. I'd suggest that the case for "world" meaning the world of the unsaved in John 12 is not as clear as you take it to be, and even its use in John 3 is probably more nuanced than you think. You might want to take a look at my treatment of John 3:16 in the following article: Limited Atonement, part 20. It seems to me that John's use of the world "world" is frequently quite loose, and that it sometimes shifts within a passage.

In John 12:47a, I take "world" to mean either the created order, or the human race non-specifically, by which I mean to say that Jesus saves both the universe and the human race by saving a remnant of humanity and destroying the rest. The concept of "saving the world" is often shorthand in the Bible for "purifying the world by saving the good and purging the evil." In the case of people, this does not mean that every individual will be purified and saved, but rather that the believers will be purified and the unbelievers will be "purged" by being destroyed and removed from the world. Compare, e.g., the freeing of the creation from its slavery to corruption (Rom. 8:21) by its destruction (2 Pet. 3:7) and subsequent renewal (Rev. 21:1-5). Many elements of the fallen world will not be present in the renewed world -- the purging and renewal will remove the evil elements from the world.