"Presbyterian moderator David Coster wrote the letter as he felt the media and politicians unfairly criticised Matthews. .
"The bishop is being blamed in a way that all the Christian denominations felt was unfair. We have remained silent until now," he said.
Coster said the letter was written independently.
"The bishop has had nothing to do with this whatsoever," he said.
"We wanted to say publicly to the bishop and the community we serve that we are concerned about how she has been treated."
The letter states church buildings are primarily places of worship.
"The costs – spiritually, emotionally and financially – of all our buildings are borne by those for whom these places of worship are their spiritual home," the letter states.
"First and foremost the Cathedral in the Square, like all Christian church buildings, is a place of worship to the God we know in Jesus Christ and a reminder to the wider community of God's presence. The reason why all churches exist is to make Jesus Christ known and to enable people to gather in community and worship. The church is not primarily a landlord tasked with caring for stone or wooden edifices."It was signed by Coster, Methodist district superintendent Kathryn Walters, Catholic diocese administrator Rick Loughnan, Grace Vineyard Church senior pastor David MacGregor, Elim Church lead pastor Nu Telea, Salvation Army divisional commander Ivan Bezzant, King's Church senior pastor Ken Shelley and Baptist regional mission leader Maurice Atkinson."