I paid my credit card on the 31st day after the payment due date, and the credit union reported that I made a late payment to a credit reporting agency. Can the credit union do that?

Generally, yes. Whether a payment is late is determined by your credit card account agreement, which is the contract governing your credit card account.  The credit union would have provided this agreement to you when you opened the account. As long as the information is accurate, the credit union can report its experience with your credit card account, including late payments.