No they can't. First, passages that speak of God's love for all the world or Christ being given to all the world have nothing in the context to limit that application in anyway. Second, even if we buy into the idea that it means "Jews and Gentiles" that still includes everyone. The only way you can make your case is to then take another step to "only some Jews and Gentiles" and that is wholly illegitimate. You can't turn "world" into "some" in those contexts and the most authoritative Greek lexicon says that "world" means "all humanity" in those passages. In 1 John 2:2 it clearly means the whole world. Does that include Jews and Greeks? Of course, because it includes everyone. But that is not even an issue John is addressing. That epistle is not concerned with the Jew/Gentile issue, and that verse has nothing at all to do with distinctions between Jews and Gentiles as people groups. It has to do with distinctions between believers and non-believers.
The only other use of "whole world" in 1 John is in 5:19 which has reference to the entire sinful world that is under control of the evil one. But Calvinists ignore this and focus on 1 John 2:15 and try to cast doubt on 1 John 2:2 meaning all of humanity because 1 John 2:15 says we should not love the world or anything in it. But then John makes it very clear that he means the sinful desires and lusts of the world. But even there, John is describing the sins of the world that we should not embrace, and in 1 John 2:2 John says that Christ died for the "sins of the whole world." Sins are committed by people. They are not autonomous entities.
So the "whole world" lies under the enemy's control and it is this sinful world that believers should not embrace, and it is the sins of this whole world that Jesus made propitiation for in His death.
John 12 is even more decisive and perfectly parallels John 3:16-18,
"I have come
into the world as a light, so that no one who believes in me should stay in darkness. As for the person who hears my words
but does not keep them, I do not judge him.
For I did not come to judge the world, but to save it.
There is a judge for the one who
rejects me and does not accept my words; that very word which I spoke will
condemn him at the last day." (John 12:46-48)
The implications of Jesus language are unavoidable. He came to save the world which includes those who will ultimately reject Him and be condemned as a result. What reason does Jesus give for not judging those who reject Him? Because he did not come to judge "the world" but to save it. That means that they
must be part of the world He came to save, otherwise his words lose all meaning.
Jesus came to save those who would ultimately reject Him and be condemned as a result.
Now compare this passage with the specific language of John 3:16-18,
“For God so loved
the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. For God
did not send his Son into the world to condemn the world, but to save the world through him.
Whoever believes in him is not condemned, but whoever
does not believe stands condemned already because he has not believed in the name of God’s one and only Son.
The parallel language is striking and deliberate. We have every reason to see world as all inclusive and no good reason to see it as limited in some contrived way as so many Calvinists insist.
And again, even if the Calvinist wants to say that world means "Jews and Gentiles" that still includes everyone. Even James White had to admit this in a debate. When he was pressed on this he ran off to Revelation which doesn't even use the term "world" and is just a description of those who are saved being saved from every tribe and nation. That text does nothing to support his case, but it does illustrate that even James White is prone to "jump" to other passages of Scripture to try to support his interpretations, something he often ridicules Arminians for doing with regards to looking at John 12:32 to help understand John 6:44, etc.