For a man renowned for his civility, the language was blunt. During his annual speech to the Anglican Church’s Sydney synod, Archbishop Glenn Davies told supporters of same-sex marriage to “please leave us”.

“My own view is that if people wish to change the doctrine of our church, they should start a new church or join a church more aligned to their views,” he said. “But do not ruin the Anglican Church by abandoning the plain teaching of scripture.”

In a report published on the Sydney Anglicans website, Davies’s media manager, Russell Powell, said the archbishop had received a standing ovation at the end of his address – as indeed he had.

But in pockets of the hall, there was also discomfort, if not with the core sentiment then with the tone. Davies has long been frustrated by what he believes is the excessive liberalism or tolerance of other Australian bishops towards same-sex relationships, particularly among clergy.

Now he watches as two relatively small parts of the church – the dioceses of Wangaratta in Victoria and Newcastle in New South Wales – are moving to bless same-sex marriages.

Pro-gay marriage Anglicans are walking a fine line in the Australian church. Some want a full marriage rite, such as the one that exists in the Episcopal Church of the US. Others, such as the members of the Wangaratta synod, have voted to bless same-sex marriages conducted under civil law. To Sydney’s “guardians” (their word) of orthodoxy, it is a distinction without difference.

One leading Sydney Anglican – supportive of but frustrated with Davies – could not work out if the archbishop’s call to “please leave” was a statement about “discipline within the church as opposed to grace outside it”. Was he simply insisting that bishops and priests stop agitating for the church to accommodate same-sex marriage? Or was the leader of Australia’s most powerful Anglican diocese, in an unusually intemperate spray, shunning gay Christians at the door of the church?

It took Davies four days to clarify that his imprecise comments were directed at the bishops, not the parishioners, but the hurt has been profound, especially for those working in Anglican education and social services.

This is a critical moment for Australia’s churches. They are attempting to persuade the federal government to accommodate their demands for greater religious freedom, including the right to hire staff whose lives accord to strict biblical views of sex and sexuality. At the same time, they insist they welcome LGBT students into their schools and gay Australians to use their welfare services.

The archbishops of the important Melbourne, Brisbane and Perth dioceses rushed to say that no Christian or searcher, regardless of sexuality, would be turned away from church. Perth’s Kay Goldsworthy, often mentioned as a future primate of the Australian church, lamented that “it is troubling that the welcome is not universal”.

The irony in all of this controversy is that Sydney’s position – stripped of its incendiary and exclusionary language – is broadly the position of the Anglican Church of Australia. On Saturday Melbourne’s Anglican synod expressed “regret” at Wangaratta’s decision and referred the issue to a church tribunal.

The church consensus on the issue is best personified by Goldsworthy and her Melbourne counterpart, Philip Freier. Goldsworthy voted yes in the 2017 marriage plebiscite, Freier no. But outside Sydney – where the diocese pumped $1m into the no campaign – the church adopted a neutral position.

The church accepted the 62% vote in favour of same-sex marriage but, in the perennial Anglican way, set up a committee to study the way it would handle the issue, before a special national meeting next year. Not even Goldsworthy said she would challenge the church’s official marriage doctrine.

On issues of sexuality and women’s ministry, the Sydney diocese is increasingly out of step with the church in the rest of Australia and certainly in the US, Canada, New Zealand and much of the UK. But it has reached into the church’s growth areas – Africa, Asia and Latin America, known as the “global south”.

Sydney was the progenitor of an organisation called the Global Anglican Future Conference, or Gafcon, which enforces a strict reading of scripture. Most of Gafcon’s member churches remain within the official Anglican communion, recognised by the Archbishop of Canterbury.

But more ominously for the worldwide Anglican family, the Sydney diocese has a history of supporting schismatic churches, not endorsed by Canterbury. At the weekend, several Sydney bishops flew to New Zealand to consecrate a bishop not recognised by the official NZ church. They have done the same with the breakaway Anglican Church of North America.

Most notoriously – decades before the controversies over sex, sexuality and even feminism – Sydney supported the Church of England in South Africa. It was a largely, if not officially, white breakaway movement from the official Anglican Church of Southern Africa. In 1997, CESA’s leader begged forgiveness before South Africa’s Truth and Reconciliation Commission for its inadequate response to the apartheid regime.

The Sydney diocese is also on the cusp of dominating the Australian church. Its evangelical theological college, Moore, is a powerhouse, churning out a couple of hundred graduates every year. These are the men – and increasingly women – who are ordained as priests and deacons, not just within the diocese but around the country.

Other colleges with more liberal or pluralist views of scripture, such as Ridley and Trinity in Melbourne, simply cannot match the numbers.

And with numbers comes power. At the 2017 national synod, Sydney and its allies in the dioceses of Tasmania, Armidale, North West Australia and segments of Melbourne and Adelaide, secured a narrow majority on the powerful standing committee.

Pessimistic liberals believe Glenn Davies’s harsh words – “please leave” – betray a deeper motive – to claim the name “the Anglican Church of Australia” and as much property as possible, push out all liberals and even moderates and then split more formally from the worldwide communion under the Archbishop of Canterbury.

Writing in the June edition of the diocesan newspaper Southern Cross, Davies emphasised that the constitution of the church “does not tie us to Canterbury” but only to those churches with doctrine that is consistent with the so-called “Fundamental Declarations” – the Bible, the 1662 Book of Common Prayer and the Thirty-Nine Articles. Sydney has also boycotted the Lambeth Conference, called every 10 years by the Archbishop of Canterbury and considered a critical symbol of Anglican unity.

Moderate evangelicals doubt Sydney wants to formally split from Canterbury, pointing out it might not then be able to call itself “Anglican” and hold on to all its property without a fight in the civil courts.

In largely secular Australia in 2019, that’s the last place any church would want to be.

• Andrew West is the presenter of The Religion & Ethics Report on ABC Radio National