An Australian Primate rebuked Archbishop Glenn Davies and Bishop Richard Condie for attending the ceremony, saying the new role doesn't align with his National Constitution and the Church doesn't approve of the move.
Rev Canon Andy Lines' new role emerged after GAFCON was disappointed in the Scottish Episcopal Church's (SEC) decision to allow same-sex marriage last month.
However, Archbishop Glenn said he knew people would "disagree and disapprove" of his participation in the ceremony, but the Scottish vote as "amounts to another significant and sad moment in the life of the Anglican Communion".
He wrote in a letter: "As you will all know, I consider such an action to be a travesty of the rule of Christ, of the doctrine of the Book of Common Prayer, and therefore an abandonment of the principles of Anglican doctrine to which we have committed ourselves."
Archbishop Glenn added that he did not take the decision to attend the consecration lightly and did not want to cause division by his action.
He said he hoped Bishops would "rally to defend the Bible's teaching on marriage, not merely for the sake of correct doctrine, but that we might preserve the message of the gospel for the salvation of all."
Bishop Richard also explained his reason for attending the event.
In a letter to the Bishops of the Anglican Church of Australia, he wrote that he felt the need to" stand in solidarity with faithful Anglicans across the globe" especially "for those who are marginalised because of the doctrinal unfaithfulness of their bishops".
He continued: "The Primate has counselled me against participation the grounds that it may impair my fellowship with you. This potential consequence grieves me... I ask that you judge me by my intentions, which are to stand in solidarity with those who will act to protect the gospel of Christ."