No need for it to be so complicated. Magnets will work just fine.
I would add some small stops to the lower part of the face of the stand so that the bottom edges of the doors have something to rest on. This will support the weight of the doors and help you keep them aligned so they look nice when closed. You also don't need strong magnets. You only need to keep the doors from falling off, which will require very little force. The stops at the bottom will do the rest of the work.
I would add some small stops to the lower part of the face of the stand so that the bottom edges of the doors have something to rest on. This will support the weight of the doors and help you keep them aligned so they look nice when closed. You also don't need strong magnets. You only need to keep the doors from falling off, which will require very little force. The stops at the bottom will do the rest of the work.