Does God love everybody (or everything)? I found D. A. Carson’s Categories in The Difficult Doctrine of the Love of God very helpful here. He breaks God's love into 4 parts.
1) God’s providential love over all that he has made - God loves birds, and cows, and insects, and even cats. God loves inanimate objects like mountains and iron.
"God creates everything, and before there is a whiff of sin, he pronounces all that he has made to be ‘good’ (Gen. 1). This is the product of a loving Creator…The birds of the air find food, but that is the result of God’s living providence, and not a sparrow falls from the sky apart from the sanction of the Almighty (Matt 6). If this were not a benevolent providence, a loving providence, then the moral lesson that Jesus drives home, viz. that this God can be trusted to provide for his own people, would be incoherent.” (16-17)
2) God’s salvific stance toward his fallen world - Can you say to your nextdoor neighbor who doesn't know Christ, “God loves you”? In one sense, yes!
"God so loved the world that he gave his Son (Jn 3:16). I know that some try to take cosmos (‘world’) here to refer to the elect. But that really will not do. All the evidence of the usage of the word in John’s Gospel is against the suggestion…However much God stands in judgment over the world, he also presents himself as the God who invites and commands all human beings to repent.” (17-18)
3) God’s particular, effective, selecting love toward his elect - Really this love is the most emphasized. This is the love that saves. God loves his creation, but there is a saving love towards his children. Those who are trusting in Christ as Lord and Savior.
“The elect may be the entire nation of Israel or the church as a body or individuals. In each case, God sets his affection on his chosen ones in a way in which he does not set his affection on others.” (18)
4) God’s love is sometimes said to be directed toward his own people in a provisional or conditional way—conditioned, that is, on obedience. Does God love me less if I sin? No, you don’t ever stop being his son or daughter. But does your sin displease God and your obedience please God? Yes.
“it does not have to do with how we become true followers of the living God, but with our relationship with him once we do know him. ‘Keep yourselves in God’s love,’ Jude exhorts his readers (v. 21), leaving the unmistakable impression that someone might not keep himself or herself in the love of God."