The blood of Jesus pays for our sins. 1 Timothy 2:5,6, “…the Man Christ Jesus, who gave Himself a ransom for all to be testified in due time.” This testimony has been delivered to those whom God has called to be part of the Church class. The rest of mankind will receive this testimony at the general resurrection. Acts 15:16-18 (NLT), “Afterward (after the church class is complete) I will return and restore the fallen house of David (Israel). I will rebuild its ruins and restore it, so that the rest of humanity might seek the LORD, including the Gentiles–all those I have called to be mine. The LORD has spoken– he who made these things known so long ago.”
Until the world accepts Jesus, they continue under the curse received as a result of Adam’s sin. Genesis 3:16-19 (NKJV), “Cursed is the ground for your sake; In toil you shall eat of it all the days of your life…In the sweat of your face you shall eat bread till you return to the ground, for out of it you were taken; For dust you are, and to dust you shall return.”
Hence we are born into Adam’s sin and conceived in iniquity – Psalm 51:5 (CSB), “I was guilty of sin from birth, a sinner the moment my mother conceived me.”
Historically, God did teach that illegitimate children could not enter the assembly of Israel as was written in the Law. Deuteronomy 23:2, “A bastard shall not enter into the congregation of the LORD; even to his tenth generation…” The Lord could not give a king to Israel from the line of Judah and Tamar until their offspring reached 10 generations; hence David is the 10th generation from Tamar. But Christians are not under Israel’s Law Covenant. Our relationship with God is through the blood of Jesus, and thus this prohibition does not apply to Christians.
Respecting modern curses, no scripture teaches that a Christian should ever curse another person. On the contrary, we are commanded to love (not curse) our enemies. Jehovah will not honor another’s curse. And if someone were cursed using a different god (other gods are all demons), that person should have faith in the one true God. Jehovah is omnipotent, all-powerful. God can and does protect His children from men’s curses.
As far as the curse of Ham goes, please note that Ham was not cursed. For a more detailed study, read the free PDF booklet: The Bible Does Not Teach the Curse of Ham