Atheist hymns are oxymoronic.

There are many love songs that express honest passion and commitment that can be used in lieu of religious platitudinous hymns.

I think that hymns can be taken as musical expressions in and of themselves without having to refer to deities, rituals, and all the religious trappings that go with them. Many of them are beautiful and my preference is for the African-American ones.

I think that the notion of interjecting religious aspects into a wedding service is really a red-herring and are really irrelevant to the ceremony. If a hymn fits, why not use it for its appropriateness to the vows of the couple being married? If not, who needs it.