When reading the runes on big issues, it is natural to turn to big events. So comment on the future of multiculturalism tends to centre on home-grown Islamic terrorism or riots in Paris's poor banlieues. However, it is often in the small details that we see the meaning of the wider picture. So I found last week, when a central problem with cultural diversity became clear after thinking about the etiquette of tipping.

I was in Vernazza, a picturesque village on Italy's Ligurian coast. I'd been there a few days and I realised that not only had I not been tipping at restaurants, I hadn't even been thinking about it. This is odd for me: like many tourists I often try to find out what the local conventions are on gratuities, but I always feel a little mean if I don't leave anything, even if I know that's the norm.

I might have been tempted to take this as a good sign of my well-developed sensitivity to local practices and traditions, but then came the thought that led me deeper: if people here are used to serving people from around the world, aren't they also used to people tipping according to their local customs, not Italian ones? If so, would my failure to leave a tip strike them as rude?

So I asked a waiter - or rather my partner, who is Italian, did: what happens here with tips? The answer was that Italians almost never left anything, Germans tended to give just a euro or two, British people usually tipped better, but Americans gave the most of all. So what did he think about Americans who didn't tip? "Tirchi" he replied - they're tight.

That little comment opened up a critical issue for me. What it showed is that "respecting the difference" of other cultures is often based on a misguided sense of how different they really are in the first place. Cultures are not hermetically sealed from each other. Every encounter we have changes both us and the people we interact with. In places such as Vernazza, it is romantic twaddle to think you are dealing with people whose values and practices are purely Italian, as set in stone sometime between La Dolce Vita and Pao lo Rossi lifting the world cup. They are us much citizens of the world as we are and, far from being offended by being tipped according to our standards, they now expect it.

The wider significance of this should be clear. Too often, well-intentioned multiculturalists like to treat "other" cultures as though they weren't really part of the interconnected world like "ours" is. "Respect" means acting as though, for example, all Sikhs had the same mindset as their ancestors in Punjab and had absorbed nothing from a lifetime in Pollokshields. Far from being respectful, this is actually insulting. It is like saying that we, the respectful cosmopolitans, are capable of adapting our behaviour to fit in with others, but those same others must be assumed to be incapable of doing likewise. It reduces minority cultures to the level of anthropological curiosities, to be treated like children.

The right view is that cultural interaction is always a two-way exchange. It is not just wrong but incoherent to insist that minorities adopt the beliefs and practices of the majority, because the majority do not have a single, settled tradition anyway. But it is equally wrong and incoherent to believe that, therefore, minorities should be left undefiled by "our" ways. The impurities have already been introduced, because pure, unchanged cultural and religious traditions are the inventions of racists. Except, that is, in the case of other cultures, where the bigots are paradoxically joined by many liberals keen to display their acute cultural sensitivity.

This is of more than mere sociological interest - it also has political implications. Policy in a multicultural society cannot be based on insisting that everyone simply sign up to a mythical, eternal set of "British values", as determined by some official process. But nor can it rest on a desire to respect the equally fantastical, fixed culture of minorities. As Italian fish and chip shops and deep-fried pizza show, immigrants change themselves, their descendants, and the country they come to. True respect for difference requires an awareness that others are as capable of adapting and changing as we are ourselves.