[raxxorraxor]

State or religious marriage is a relationship with an authority. You can swear eternal loyalty to anyone and however many people you want to without any of that.

Primarily state marriage is about sharing privileges and duties before the law.

[lanternfish]

While this is true on a purely de jure interpretation of the dynamics at play, a more clear-cut example - like same-sex marriage - makes it clear that the "right to marriage" includes not only the right to life-scale commitment to a person(s) but also the right to have that commitment recognized by the state. Insofar that marriage as a legal construct carries additional privileges alongside the simple recognition, which it does, the "right" to marriage must also include the "right" to access the consequent privileges or you have a structure of authority stripping those privileges by omission.