Weren’t converts permitted to enter Judaism in the OT? While the Jews did not go out to seek converts, they certainly let them in. Why, then, do the people of Israel turn these men away?
First, there is a difference between converting to the God of Israel, and building the Temple to the God of Israel. While these men would be allowed to come to faith in the living God, they were not permitted to build the Temple. By allowing them to build the Temple, they would have profaned it.
Second, these people turn out to be evil. Perhaps Zerubbabel saw that these men were not genuine, having false motives. In fact, we see this in verse 4. After being shot down, these men try to stop the Hebrews from rebuilding the Temple. They even hire men to stop the Jews from accomplishing their building project (v.5-6)! They tried to write to Artaxerxes to frustrate the project. We read in verse 13: “Now let it be known to the king, that if that city is rebuilt and the walls are finished, they will not pay tribute, custom or toll, and it will damage the revenue of the kings.” These men were probably just trying to get the Temple to pay tax. Later, when they rat these men out to Artaxerxes, they claim that the Jews were planning on withholding taxes from the king.
Third, Zerubbabel showed excellent discernment. Put yourself in Zerubbabel’s shoes. He is just beginning to reconstruct the Temple. It’s a supernatural event that this is even possible. All of a sudden, some Gentiles come to offer their help. It must have been tempting to take them up on their offer. Instead, he discerned that they were enemies. If he had let them in on the project, it may have been worse.