It had nothing to do with the church or ceremony part. It had everything to do with the principle of calling it something other than Marriage that is afforded to same sex couples. Is my marriage to my wife a civil union because I don't believe in an Christian or Abrahamic God? Is it any less legally recognized as a marriage because of that?
The obvious and simple answer is to no longer civilly recognize "marriage" leave that to religious or "ethical humanist" organizations. Have anyone who wants to do so register their "partnership" - with a JoP for the purpose of property/children/financial rights, etc. Marriages would be simply a function of the couples and their religious or other institution. This strips away the "validate me" reason that really is the motivation of many gay marriage groups. Just as one shouldn't be oppressed one should not seek, need, or be granted "official" government validation of their private lives.