The Rev Prebendary Kay Garlick has called on the Synod to be a model of how Christians can "disagree in love" as it debates plans for women bishops.
The Synod has already agreed in principle to ordain women as bishops. Some 1,300 clergy have threatened to leave the Church over the issue.
Unbroken chain
Traditionalists from the Anglo-Catholic wing of the church want the right to opt out of the jurisdiction of a women into special dioceses headed by male bishops, or at least to have guaranteed access to male bishops.
HAVE YOUR SAY
There's no reason why a woman can't do the same job as a man. Then we will see the Church split as it inevitably will with all these changes
M, Cambridge
BBC religious affairs correspondent Robert Pigott says the Synod faces an awkward decision about how to treat traditionalists whose religious consciences will not allow them to serve under a women bishop.
He says the Anglo-Catholic Anglicans argue that Jesus chose only men to be his immediate 12 apostles, the men who were given leadership of the early Church.
They point out that an unbroken chain of male bishops has led the Church since then.
Our correspondent says they believe that a man ordained by a woman might not be properly ordained, and might not in reality be a priest.
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Right Rev Martyn Jarrett believes it would be 'un-Catholic' to allow female bishops
Such a suggestion is strongly rejected by women priests and many others in the Church.
However, the traditionalists could still get their own way, our correspondent says.
They have formed an alliance with evangelicals who have their own biblical reasons - the belief that men should have authority over women - for demanding the imposition of special conditions before women are ordained as bishops.
Conversion debate
Speaking at the opening meeting in York, Ms Garlick, from Much Birch, Herefordshire, acknowledged the outcome of the debate over women bishops would inevitably bring "hurt" to some members.
But she said the Synod should present a model of how Christians who disagree can respect and care for each other.
Meanwhile, a traditionalist Synod member has accused officials of suppressing his call for an explicit policy of converting people of other faiths, including Muslims.
Paul Eddy's motion was backed by about a quarter of the Synod, but officials say the agenda was too crowded.
The Fellowship of Confessing Anglicans - the international alliance of traditionalist Anglicans formed in Jerusalem last week - has made the duty to evangelise other faiths one of its key policies.
The General Synod will also hear a presidential address on Saturday from the Archbishop of York, Dr John Sentamu.