it is not the business of the State to tell them who they can marry
It is the business of the state, and it does it all the time. You can't marry someone who is already lawfully married, you can't marry someone under age, you can't marry someone you've adopted, you can't marry your ancestor or your descendant, you can't marry your brother or sister, you can't marry someone who is mentally incapable of understanding the process, you can't marry someone without their proper consent etc etc. What makes any of these different. They are just social constructs after all. Ultimately the state can and will dictate who you can marry based on whatever social mores are in place at the time.