Except marriages and divorces are recognized in every state.
Each state did decide about the legality of slavery until the passage of the 13th Amendment. (I have to wonder how an Amendment guaranteeing a right to abortion would be worded).
As to marriages and divorces, the Constitution require that each state recognize the official actions of another state. So if you’re legally married in one state, you are legally married in another state, even if your marriage wouldn’t be legal under your state’s laws. This is why people were upset that some states were toying with the idea of legalizing gay marriage, before SCOTUS in its infinite wisdom took that decision away from elected legislators.
Divorce used to be difficult to nearly impossible to obtain in some states, especially New York. But Nevada only required a few weeks residency for someone to file for divorce. Movies in the 40s and 50s would make reference to this by “she moved to Reno”. Get the divorce under Nevada law and you are divorced in NY.