I don't think I suggested that only a "religious figure" could perform marriages; it's not my business what anybody else considers to be a valid marriage ceremony.

Marriage means whatever the couple getting married say it means. If they say it means a Catholic mass presided over by the Bishop, and they have that, then they're married. If they say it means a civil union ceremony presided over by a judge, and they have that, then they're married. If they say it means a party in the back yard for their friends presided over by a portrait of Bugs Bunny, and they have that, then they're married.

I'm not suggesting for a moment taking the word "marriage" away from non-religious people (among whom I count myself). I'm only suggesting taking the word "marriage" away from the State.