Why did the Jewish believers in Jerusalem think Gentile believers needed to be brought under the law?

They were still saturated with the law of Israel and could not fathom that the God of Abraham would save Gentiles without also placing them under that same law. Like Judaizers, they taught that circumcision according to Moses was necessary, insisting Gentiles could not be saved otherwise.

Les explains that the Jewish believers in Jerusalem were still so saturated with the law that they tried to bring the Gentile believers of Paul’s ministry at Antioch under it. They could not fathom that the God of Abraham would go to those pagans and bring them to salvation without bringing them under the law of Israel. Acts 15 shows certain men from Judea teaching that unless Gentiles were circumcised after the manner of Moses, they could not be saved. This was the Judaizer opposition Paul faced while bringing the gospel of the grace of God.

Why did the early Jewish believers have trouble accepting Gentile converts who were not under the law?

They were so saturated with the Mosaic law that they could not conceive of God saving Gentiles without first bringing them under Israel's law. They believed circumcision and law observance were necessary for salvation, as Judaizers from Judea insisted at Antioch. Jewish believers in Jerusalem tried to bring Paul's Gentile converts under that law.