From what I understand Roman law had two very significant statutes regarding religion:
a law requiring that the Roman deities be acknowledged by a periodic sacrifice
a law permitting Judaism to operate as a legal religion
In addition there were ad hoc requirements made that the Jewish temple display Roman artifacts or offer sacrifices for the emperor and such.
Since Herod Agrippa was King in Judea would he have been involved in dealing with such cases and imposing the will of Rome on Jewish and Christian religion?
For example, would Herod be responsible to make sure that Jews and Christians made sacrifice to Roman gods? Would he have to decide if someone had properly recanted for being a Christian? Would he have been responsible to enforce the emperor's requirements of Roman symbols in the temple, etc.?
[Act 12:1-5 ESV] (1) About that time Herod the king laid violent hands on some who belonged to the church. (2) He killed James the brother of John with the sword, (3) and when he saw that it pleased the Jews, he proceeded to arrest Peter also. This was during the days of Unleavened Bread. (4) And when he had seized him, he put him in prison, delivering him over to four squads of soldiers to guard him, intending after the Passover to bring him out to the people. (5) So Peter was kept in prison, but earnest prayer for him was made to God by the church.
NIV Revelation 2: 12 “To the angel of the church in Pergamum write: These are the words of him who has the sharp, double-edged sword. 13 I know where you live—where Satan has his throne. Yet you remain true to my name. You did not renounce your faith in me, not even in the days of Antipas, my faithful witness, who was put to death in your city—where Satan lives.