The woman caught in adultery wasn't state sponsored. A women taken in adultery would be taken before local elders or a Jewish court: An accusation could be brought before local judicial authorities. The Torah describes judges and elders handling legal disputes (Deuteronomy 19:15–18).or before the Jerusalem authorities in certain cases: Later Jewish legal traditions describe suspected adultery cases being referred to the Great Sanhedrin in Jerusalem. The Mishnah, Sotah 1:3–4, discusses this procedure.I don't think Matthew 25:30 addresses the point I raised. Christ's final judgment of souls and the state's execution of criminals are not the same thing.
They would sometimes taken to the Temple in the specific ordeal described in Numbers 5:11–31: This was a distinct procedure for a husband who suspected his wife of adultery but lacked proof. It was not the standard destination for every woman caught in the act.
In this case,they had a lynch mob take her to Jesus, who was teaching in the temple and not operating in an official priestly capacity. The whole event was to snare him so he could be accused.