The famous Amazon ad showing the friendship of a vicar and an imam has been a resounding Christmas success for the retailer, managing to hit the sweet spot of feel-good sentiment, genuineness and commercial nous that adds up to advertising gold.

Rev Gary Bradley, vicar of Little Venice, Paddington Green, and Imam Zubier Mohammad, principal of a Muslim school in Leicester, followed up their ad with a live interview on Al Jazeerah English. Were they a real vicar and imam rather than actors, as some had assumed? Yes. And were they really friends? They'd never met before the ad was filmed, but they formed an instant bond. Their warmth and mutual respect shine out of their conversation, in which there's a disconcerting tendency to finish each other's sentences.

In the context of everything that's going on in the world today, the ad, and more particularly the interview, have a dislocatory quality. Especially in recent times, Muslims are often depicted as the enemy. In the UK, the government's Prevent strategy has, some have argued, the effect of portraying them all as potential terrorists. In the US, Donald Trump has made various wild statements about them and has tapped retired Lt Gen Michael Flynn as his national security adviser. Flynn has said "fear of Muslims is rational" and likened Islam to "a cancer".

As well as the challenge to the "Muslims-are-terrorists" fallacy, the conversation between Bradley and Mohammad is also a challenge to the way Christians and Muslims interact theologically. And this is a far more complicated knot to unravel.

In a nutshell: both Islam and Christianity are mission faiths. Christians and Muslims both believe their own faith is the right one and they are committed, in principle, to helping other people see that. They might talk the language of respect and tolerance, and there are those in both faiths who think that all religions lead to God and are relaxed about who chooses which path. Certainly Islam and Christianity have more in common than Christianity and Hinduism, say; they can talk the same religious language, though they might say very different things in it. But at the core of each faith is a rock-hard conviction: for Islam, that there is one God and Mohammad is his prophet, and for Christians, that God was incarnate in Jesus Christ.

So how, especially in a multi-cultural society in which people of different faiths are likely to meet each other in all sorts of different contexts, is this contradiction to be managed? I want to suggest three things.

First, respect.

In WB Yeat's poem Aedh Wishes for the Cloths of Heaven, there are the lines: "I have spread my dreams under your feet; Tread softly because you tread on my dreams." It's a love poem, but religion is something of a love affair too. When we meet someone from another faith and explore it with them we are treading on their dreams, and we need to tread softly. They are not our dreams, but that's not the point: no matter how strongly we disagree with them, they may feel as committed to their faith as we do to ours. That's why language like that of Franklin Graham, who has repeatedly described Islam as a religion of war and a global threat, has to be resisted. He is talking about people like Zubier Mohammad, an elderly man with dodgy knees who appreciates a gift of kneepads via Amazon. If those who stoked anti-Muslim feelings during the recent US election campaign – and the British EU referendum – could learn to see Muslims first and foremost as people, made in the image of God, they would be more inclined to tread softly.

Second, politeness.

It's an under-rated virtue, theologically speaking, but worth cultivating. A few years ago I blew a large hole in the household budget with a holiday in India. Our guide was a devout Hindu who took us to visit a temple dedicated to the goddess Kali. The congregation was waiting entranced, singing a low, repetitive chant in front of a closed curtain. The curtain was drawn back and the crowd exploded into a shout of rapture as the image of Kali was revealed: clearly it was a moving and meaningful experience for them.

As we left, our guide draped garlands of marigolds around our necks and told us we shouldn't just discard them; they had been dedicated to the goddess and had to be laid beneath a particular tree.

I didn't decline the garland because it had been devoted to a goddess in whom I don't believe, and at the end of the day I didn't just throw it away; I gave it to our driver to dispose of reverently, and if I could remember which tree to lay it under I would gladly have done so myself. The point wasn't what I believed, but what our guide did. And there's no possibility of a genuine conversation without genuine politeness.

Third, integrity.

We can be respectful and polite as Christians, but we cannot pretend to be anything other than we are. If we believe God was incarnate in Jesus and in no one else, we are making a huge truth-claim about our faith that is in the end exclusive. As the great missiologist Lesslie Newbigin once wrote: "The relativism which is not willing to speak about truth but only about 'what is true for me' is an evasion of the serious business of living. It is the mark of a tragic loss of nerve in our contemporary culture. It is a preliminary sympton of death."

For evangelical Christians, witnessing to our faith is essential. But how should we do it?

Newbigin also wrote this advice: "Live in the kingdom of God in such a way as to provoke questions to which the gospel is the answer." So we should be prepared to answer questions about our faith, at the same time as resisting programmes and techniques ("10 Ways To Convert Your Muslim Friend!"). Politeness means not forcing our faith on someone. Respect means having a ready answer when they ask about it.

There is a large amount of faith and trust involved in inter-faith encounters. Evangelical Christians would want to affirm that Christ calls everyone to repentance and faith in him. At the same time, we can't enter a friendship with an agenda. Interfaith evangelism is not about conversion techniques. It's about becoming the sort of people who might draw people to Christ because we are like him – and leaving the result up to him.

Follow Mark Woods on Twitter: @RevMarkWoods