Why wouldn't the Temple priesthood care for the Jewish believers who were in need?
The Temple priesthood would not care for these Jewish believers because they had embraced Jesus of Nazareth, whom the Temple's religious leaders detested. With no welfare system and Israel not yet fully set aside, these destitute believers were isolated, so their only hope was the collection from Gentile believers, sent to Jerusalem.
Les explains that at this point Israel had not been totally set aside; the Temple was still going, and Israel was still in the land. These Jewish believers were destitute and had no welfare system, so they were in an island of need. The Temple priesthood certainly was not going to take care of them because they had embraced Jesus of Nazareth, whom these religious leaders detested. Their only hope was the collection from the Gentile believers as it would be sent to Jerusalem. Earlier, the duty was clear: if Gentiles had been made partakers of Israel's spiritual things, then Gentiles also had the responsibility to minister to the Jews in carnal or material things.