TL;DR I was able to order the MacBook with gift cards after talking to four Apple Support specialists for over three hours and waiting an extra day to get an update.
I had the same issue when using multiple gift cards while purchasing a MacBook. I'm still astounded by Apple Support's uselessness in fixing this issue. I talked to four different support specialists for over three hours (including wait times) who all had no idea why this was happening. The first specialist transferred me to a sales specialist who gave up and transferred me to another specialist. The second specialist "guessed" that the gift cards were blocked due to a possibility of fraud and asked me to take photos of (1) the front/back of the gift cards and (2) the receipts. I sent all of the requested photos and screenshots, only to be transferred to another "Gift Card" specialist who could supposedly help me. The third specialist informed me that the gift cards were valid and didn't understand why the error message was popping up. So she transferred me to another specialist. The fourth specialist also didn't have any clue. As a last resort, she asked me for PIN numbers of the gift cards so that she could submit a request to people who have access to the backend system.
For reference, here is the error message I saw.
A day later, I received an email from Apple informing me that the issue has been resolved. There is no explanation as to why those error messages popped up.
I was able to place the order after I got this email.