Jordy
After playing around with it a bit more I realized that my issue was caused by the MasterCard 3D Secure check. As I had not verified my identity yet and my browser (Brave) was blocking all third-party scripts, the security check never popped up and MasterCard was unable to proceed.
In short: make sure that, when your identity was not yet verified by MasterCard, your privacy protecting tools (browsers, adblockers, ghostery, etc.) are not blocking MasterCard from performing this check!