Cousins can marry in Japan, if they so wishes to. Also, in the grand schemes of royalty, I don't think they care much if they're cousins.
BUT! The Kou chose Reirin exactly because she IS frail. She wasn't supposed to be chosen. They mentioned that it was to avoid excessive power on one family since the previous one is a Kou, but I guess it does well to maintain a genetically healthy heir too.
Love is not really that important when it comes to royal affairs, but honestly, Reirin should NEVER be the empress. Because if she is, she might die trying to birth a child. More importantly, since they are cousins, the child might be as frail as Reirin.
Honestly Reirin deserves to be free frolicking in the mud in the countryside.
arent the prince and reirin cousins lmfao another reason why i dislike them together. its clear the knight and reirin will end up together and hopefully keigetsu and reirins brother will end together.
The story hinted at the fact that the knight shin-u (or whatever his name is) will be awarded with the lowest ranking consort, so maybe keigetsu will marry the knight and they will remained swapped at the end of the story lol