At 7:28 +W asks, "What is that wedding garment? Surely, it's the state of grace."
In the sermon I heard for the same Gospel, my priest said that the wedding garment is the mark of Holy Baptism on the soul. He said that those who face their final judgment without the mark of Baptism will be subject to God's judgment for not wearing the necessary wedding garment.
Obviously, Baptism isn't the entire answer, for the state of grace is also necessary. However, it is by Baptism that the soul is sanctified initially by the absolution of original sin, then the person must persevere until the end to be saved.