I mailed my mortgage payment before the due date. However, the credit union received it one day after the due date, and I was charged a late fee. Can it do this?

Yes. You must mail your payment in sufficient time for the credit union to receive it on or before the due date. 

When considering timeliness of a payment, credit unions are not obligated to honor postmarked dates. In determining lateness, the credit union goes by when the payment is received, not when it was mailed.