I hosted a party last week. One of the guests raised an eyebrow at the presence of a fellow columnist noted for her less than progressive views – let’s call her Melanie. I pushed back against his surprise. She was a friend, I said. And anyway, she wasn’t close to being the most rightwing person in the room. He hadn’t met my mother yet.

The debate over Europe has once again raised the argument about keeping bad company. Lefty outers, like me, are accused of lining up with Nigel Farage and George Galloway; lefty inners with Goldman Sachs and David Cameron. “Sleeping with the enemy,” comes the accusation. For those who prefer their politics to be neatly tribal, it’s all rather unsettling. As if we are defined by the company we keep. And, as if by keeping “bad company”, there is some risk of contagion. This is the politics of the playground, where cooties can be acquired by mere proximity. NUS officer Fran Cowling won’t share a platform with veteran gay-rights campaigner Peter Tatchell because, she says, he is a “racist” and “transphobic” – claims that seem utterly ridiculous to me. But even if he is, why the childish refusal to share a platform? She won’t catch anything. “Never kissed a Tory,” read the popular Labour conference T-shirt. Well, they should give it a go.

As it happens, I kiss Tories all the time. And members of Ukip. And communists. And people of all colours, backgrounds and sexualities. “Let us offer one another a sign of peace,” says the priest in the middle of Sunday mass. Thus begins a five-minute free-for-all in which the congregation embraces each other. When the Church of England was reconceived after the bloody sectarianism of the English civil war, it was done so as part of a wider project of national togetherness. It mattered not whether you fought for the king or for parliament, you could still pray in the same pews and worship the same God. OK, there were still many excluded from this establishment – Jews, dissenters, Roman Catholics, etc – but the basic principle of the parish system was that everyone went to the local church, no matter what their theological stripe.

For centuries, this was the social glue of community, especially in rural areas. Now, unfortunately, birds of a feather increasingly choose their own like-minded flock – still, Sunday morning church remains one of the most diverse gatherings in the country. Part of the point is that I have to learn how to put up with people who are different and they have to learn how to put up with me. Yes, of course we squabble. But nonetheless, we have a connection greater than our differences. And dividing people up into the sheep and the goats is a task well above my theological pay-grade.

Talking of the animal kingdom, one of the most depressing things about researching this column was when I Googled “unlikely friendships”, only to discover endless saccharine images of dogs cuddling up with ducks and cats with squirrels. It’s perhaps a small thing, but telling. Where were the homo sapiens? And are unlikely friends somehow unnatural? Perhaps there is something freakish about the friendship between, say, the basketball star Dennis Rodman and Kim Jong-un or even Yanis Varoufakis and Norman Lamont.

But there are solid, serious examples. When staunchly conservative supreme court justice Antonin Scalia died recently, his fellow judge, the staunchly liberal Ruth Ginsburg, called him her “best buddy”. For two decades they spent New Year’s Eve together. And my wife’s “grandma”, 99-year-old Ruth Dayan, former wife of Israeli general Moshe Dayan, has been longstanding friends with Yasser Arafat’s mother-in-law, Raymonda Tawil. Despite their marital connection to sworn enemies, they often go on holiday together.

Yet in a recent poll, 28% of Labour supporters said they would be unhappy if their son or daughter married a Tory. And 19% of Tories would be unhappy if their child married a Labour supporter. “I’m the least sectarian of people,” said Labour MP Stephen Pound. “But if my daughter came home with a Tory, I’d disown her.” I hope this was said in jest. If not, it is the most petty-minded and miserable tribute to the growing partisanship of modern British politics. And if the EU debate disrupts this pathetic default tribalism, so much the better.

@giles_fraser