The General Synod of the Church of England has used the time freed up by the postponement of the debate on female bishops this week to enter into the politics of Israel-Palestine. I want to joke that it's only the C of E that, unable to sort out the simple question of whether women should be bishops, decides to tackle the problems of the Middle East. But as any column about Israel-Palestine – especially written by a Christian – places one's head immediately next to several whirring meat slicers, I am going to make this the last quip on the issue. So to the facts.

The motion that was overwhelmingly passed endorsed the work of two organisations, the Parents Circle Family Forum (PCFF) and the Ecumenical Accompaniment Programme in Palestine and Israel (EAPPI).

The first of these is uncontroversial. The Parents Circle is a joint Palestinian-Israeli organisation of more than 600 families, working for peace and reconciliation, all of whom have lost a close family member as a result of the conflict. Last month in the speaker's rooms in the House of Commons, Robi Damelin, whose son David was killed by a Palestinian sniper, told a gathering of mostly British Jews and some (but not many) Muslims, that if they hadn't anything useful to contribute to the peace process, it was better if they just shut up. Those safely living more than 2,000 miles from the conflict have no right to make things more difficult for those struggling to find common ground in the midst of so much death and suffering. Her point was well made. Indeed, the Parents Circle has acquired so much credibility for its heroic efforts at peacebuilding that few would challenge its right to say sharp things to both communities.

But EAPPI is a different kettle of fish. Last week, the chief rabbi, Lord Sacks, warned the synod against passing the motion in support of EAPPI. "It would do serious damage to Jewish-Christian relations in Britain, which have been so positive in recent decades." Following the vote, the president of the Board of Deputies of British Jews, Vivian Wineman, condemned the synod for choosing to "promote an inflammatory and partisan programme at the expense of its interfaith relations".

EAPPI is a programme set up by the World Council of Churches and currently run in this country by the Quakers, who have a distinguished record on peace and justice issues. It originated in a request made by the Jerusalem churches "for the protection of our people" and seeks to bring international volunteers to the West Bank to offer this protection for Palestinians (some of whom are Christians) through a non-violent presence, accompanying children to school, farmers in their olive fields and visitors through Israeli checkpoints. It seeks to report human rights abuses by the Israeli army and settlers and supports acts of non-violent resistance to the occupation, including boycotts.

During the debate the archbishop of Canterbury spoke of his "respect and gratitude for the immense courage and dedication of the volunteers" and said that "there are some people who, in their uncritical assumption that the Israeli government can do no wrong, are clearly going to be very irritated by … EAPPI". The gap between Rowan Williams and the chief rabbi – usually regarded as two peas in a pod – has rarely seemed wider. Which may be why, despite his obvious commitment to EAPPI, Williams supported an amendment that sought unsuccessfully to delete references to specific organisations in the synod motion.

So how far can any Christian church go in challenging the conduct of Israeli policy towards the Palestinians, many of them Christians?

To what extent does the western church's responsibility for centuries of antisemitism require that it remain silent on such issues?

The specific beef that many in the Jewish community have with EAPPI is that those who return from the volunteer programme can end up with a one-sided view of the conflict. And there is some anecdotal evidence that volunteers who have spoken to church groups about their experiences on the West Bank have not always been careful enough to distinguish criticism of Israeli policy from criticism of Jews per se. If this is the case it must be strongly challenged.

The specific brief of EAPPI volunteers is to protect vulnerable Palestinians from bullying and intimidation. This is important and necessary work. I support it. But, in itself, it does not offer a 360-degree appreciation of the situation. Where EAPPI is open to challenge is if those who return from 40 days at an Israel checkpoint believe that this qualifies them as mini-experts on the entire politics of the region. They need also to have danced on the bar in Nanuchka in secular Tel Aviv. And have seen children in Gaza handing out sweets when an Israeli soldier has been shot. And been though the heartache of failed peace and broken dreams. And a thousand thousand other experiences besides. It is here that the Parents Circle is a different kind of thing to EAPPI.

Nonetheless, the friends of Israel do themselves few favours if they insist that all criticisms of Israel's behaviour towards Palestinians are motivated by one-sidedness or hostility to Jews. I'm not saying this happens all the time. But when it does, those of us who want to be critical friends of Israel (and Palestine) find that the ground on which we stand is constantly eroded. I believe in the existence of the state of Israel and in its need for security. But the "with us or against us" approach needs to be resisted at all times. And that means holding a position that is likely to draw vociferous criticism from several different quarters. But unless this ground can be held, we concede to a dangerous binary division that can only be settled by further violence. To spell it out: critical friends have a responsibility to be both critical and to be friends.