Why did the religious section of Judaism reject Stephen's teaching about the coming King and Kingdom?
The religious leaders rejected it because Stephen's teaching about the coming King and Kingdom meant the Mosaic system of law and temple worship would fall by the wayside, replaced by the New Covenant. They viewed this as blasphemy against Moses, the holy place, and the law, and refused to change their established ways.
In the passage, certain synagogues disputed with Stephen but could not resist the wisdom and spirit by which he spoke. They then suborned men and set up false witnesses accusing him of blasphemous words against Moses, God, the holy place, and the law, saying he claimed Jesus of Nazareth would destroy the place and change the customs Moses delivered. Les explains Stephen was proclaiming the coming of the King and the Kingdom. When the King would come, the whole Mosaic system of law and temple worship would fall by the wayside, the New Covenant would become a reality, and they would no longer have to study and witness because everybody would be in right relationship with God. The religious section of Judaism responded, "Hey, no way! We're not going to let anything change the way we have always done things."