What IS our 'culture' when you get right down to it? A bastardised version of a middle-Eastern religion and a handful of 'ancient' pagan ideas,a lot of which were actually invented by Victorians who wanted a bit more romance and mystery.
Even England's patron saint is a generic 'name picked out of a hat' who never even came here and is the patron saint of a fair few other countries.
Scotland, Wales and Ireland have rather more cultural heritage than the English (and they aren't quite so inclined to mock the folk music/dancing that remains, either).
People's views on the performing of the nativity baffle me. A story about a middle-Eastern couple fleeing from their home, looking for shelter...how does anyone not see the irony. The man we worship as the son of God wasn't from these parts. Christmas isn't even when he was born, but despite that, we hang on to this as a piece of 'our' culture. And despite the rumours and outrage, the only time Christmas ever got banned was by a puritanical Englishman.
We have spent centuries invading other people's land and bringing back bits of the culture we like, whilst stamping it out in every country we colonised.
Frankly, on the subject of different cultures mixing, we are the biggest hypocrites going. We don't do integration ourselves, but by golly we expect everybody else to.