The headline was "Churches agree on incarnation after 1500 years of strife". For a pretty heavy theological piece it was surprisingly popular. To recap: it was the Oriental Orthodox Churches with their wonderful titles redolent of the Mysterious East – the Coptic, Ethiopian, Eritrean, Syriac, Malankara Syrian and Armenian Apostolic Churches – and the rather more mundane C of E. They had agreed ways of talking about the incarnation of Christ with which they were all happy. 1500 years was a bit of a stretch, as the C of E has only existed since 1534, but it inherited the Western tradition which was one half of the original argument.

Nowadays, a 1,500-year-old argument seems plain crazy. In the UK, there's more denominational fluidity than ever before. Indeed, most of the life and growth is in congregations that don't identify with the historic denominations at all. It's becoming rarer and rarer to find someone who'll say bluntly, "I'm a Methodist", or "I'm an Anglican" – particularly in the Protestant evangelical tradition. "I'm a Christian who goes to a fill-in-the-blank church" is as far as it goes.

But here's the thing: I am one of them. I have the name of my denomination running through me like Blackpool through a stick of rock. I am fiercely proud of my heritage, I think we're right about stuff other people are wrong about, and I blow my nose at people who think we should all be one super-Church. Christian unity? Up to a point, and not very far at that.

In other words, in today's terms I am a delusional dinosaur, a point made wordlessly by the pitying expressions on the faces of fellow-ministers to whom I once tried to explain myself. "What we need is not less denominationalism, but more," I said, in the manner of Lord Cardigan suggesting "Let's go that way, shall we?" The view did not find favour.

Now, I know: we wouldn't start from here. No one can read the history of the Church without wishing that things had been different. But here is where we are, and just maybe, identifying yourself proudly and passionately with one manifestation of the Church rather than another might have something to be said for it. Here's why.

First: truth matters. Those Anglicans and Orientals spent as much time as they did talking about theology because it was important. How God was incarnate in Christ is significant in a way that other things – like human sexuality – are just not. Get it wrong, and you end up with a Christ who is untouchably divine, unable to sympathise with our weaknesses, or unremarkably human, unable to save us.

Most divisions in the Church have begun in the same way: with a deep sense that something desperately important was at stake and that someone needed to rescue a truth that was having the life choked out of it by an institution. For Methodists it was the need for personal salvation and a relationship with God. For Baptists it was even more fundamental: how do you become a Christian? Are you born into the faith, baptised into it as an infant, or do you choose freely, baptised into it as a response to God's call?

For new Church movements – think Vineyard or Christian City – it was frustration at the old wineskins which were expected to contain the new wine. To be true to their own vision, their pioneers had to leave and start something new. It's said that the Apostle John found the heretic Cerinthus so alarming that he once ran out of a bathhouse, crying "Let us flee, lest the building fall; for Cerinthus, the enemy of the truth, is within!" So do we still value truth, or are we just interested in whether the chairs are comfy?

Second, we learn stuff from our spiritual ancestors. All those years, or centuries, of a particular tradition, leave their mark on our souls. Spirituality is subtly different in different places and among different people. The stories that we tell and are told, the way we learn to pray, the songs and hymns we sing, the sermons we hear – they help create a certain kind of Christian.

Of course we can learn from other traditions as well, and one of the exhilarating things about the last few years is the way that dyed-in-the-wool Protestants have learned to sing Taizé chants in Latin. But the beauty of cathedral worship, the intense biblicism of the Brethren, the richness of Methodist hymnody – they are the soil from which the fruit grows, and it needs to be cultivated and enriched through a deep connection between the community of believers and their heritage.

Third, though: if proud denominationalism – or non-denominationalism – ever becomes a way of defining ourselves over against other Christians, it's gone too far. The truths and traditions we've received from our spiritual ancestors are precious, but they're to be shared, not jealously hoarded – and if there's one thing to be said for today's indifference to history and theology, it's that these things no longer divide as they did.

In that perfect world, the Orientals wouldn't have split from the rest. The Great Schism of 1054 wouldn't have happened. Martin Luther would have nailed his 95 Theses to the Wittenburg church door and the bishops would all have said, "Do you know, you're absolutely right?" And so on.

Christians have dis-fellowshipped each other, and worse, far too easily. Byron wrote in Don Juan that "Christians have burnt each other, quite persuaded/ That all th' Apostles would have done as they did." There's a fundamental unity between Christians that stems from us being 'in Christ', joined with an indissoluble spiritual bond. Put like that, small denominational details just look ridiculous. I would gladly, for the record, worship with any other Christian at all, collaborate on any worthwhile enterprise, honour and defer to my spiritual superiors of whatever brand.

But still: our ancestors did not teach us nothing. Give me an Anglican who's a real Anglican, a Methodist who's proud to be a Methodist. And if you belong to a church that's thrown off the shackles of the past and is trying to be something new and different and emerging rather than emerged: be glad of that too, but remember that you didn't come from nowhere: find your place within the whole Church, not off to one side of it.

Difference is delightful. Let's treasure it.