This is interesting, I’m going through the Orthodox study Bible and they leave the notes under Genesis 6:2 and 4 blank. This is likely intentional as the Orthodox do not like to be over defined. They probably don’t want to dot the i or cross the t. In this way they are much like Anglicans. I know for a fact that the Roman Catholics do not believe the Nephilim were Angel/human half breeds although I do not own a Roman Catholic study Bible. I am looking at samples of the Lutheran study Bible online. For Genesis 6 verses 2 and 4.
Genesis 6:2 Sons of God = Godly believers, Sethites, from whom the promised messiah would come (Gen. 3:15). Some interpreters have considered the “Sons of God” angels, based on the expression in Job 38:7. However, such a conclusion directly contradicts Jesus’ teaching about the nature of angels (Mt. 22:30) and Moses teaching about “kinds”. Daughters of Man = Godless unbelievers, Cainites.
Genesis 6:4 Nephilim = thugs and tyrants. The first nobility in the world were a group of tyrants, but admired nonetheless. They were sinners ripe for judgement in Gods eyes.
The Lutherans make a good point and I think the Roman Catholic Church would agree with their conclusion.