Here is Dr. Mohler’s answer from his book We Cannot Be Silent. All punctuation and emphasis is his.
Attending a wedding ceremony always signals moral approval. This is why The Book of Common Prayer (which has provided the traditional ceremonial language known to millions of people throughout the centuries) contains the phrase that asks if anyone knows any cause that should prevent the marriage-“speak now; or else forever hold your peace.” These words reveal the historic function of the wedding ceremony as a gathering of celebrants who come together to grant moral approval to the union of two people in marriage. Attending a same-sex marriage ceremony is to grant a positive and public moral judgment to the union. At some point, that attendance will involve congratulating the couple for their union. There will be no way to claim moral neutrality when congratulating a couple upon their wedding. If you cannot congratulate the couple, how can you attend?