Why did the priests and Levites from all Israel move to Judah in Rehoboam's day?

Answer: Jeroboam rejected them as priests

The Levites left their pasturelands and went to Judah and Jerusalem, because Jeroboam and his sons had rejected them as priests of the LORD.

“Moreover, the priests and Levites from all their districts throughout Israel stood with Rehoboam. For the Levites left their pasturelands and their possessions and went to Judah and Jerusalem, because Jeroboam and his sons had rejected them as priests of the LORD.”— 2 Chronicles 11:13-14 (BSB)