One does not have the right to marry whoever they are in love with. The constitution does not protect the citizens from their state and federal government from that. Sick but if one is in love with a child, they do not have the right to marry that child.
That said it was brought up before, but the EPC of the 14th amendment does protect the citizens of US from their state from gender discrimination. Simple argument but Alice can marry Charles because she is a woman but Bob can't marry Charles because he is a man. That is treating Bob and Alice (and Charles) differently strictly on the basis of their sex/gender.
"No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States"
Notice it even says privileges not rights (so even if you could argue marriage is not a right, it's irrelevant it is certainly a privilege granted by their state).
And Alice, Bob, and Charles have certainly all had their privileges abridged by not allowing them to marry someone solely because of their relative sexes.