To focus more specifically on Britain, a lot of what’s considered fundamentally British are relatively recent adaptations. The first Indian curry house was opened in Britain in 1809, curries dipped in popularity in the early 20th century, only rising towards their current level of popularity in the 1970s. Christmas trees didn’t become popular in the UK until the 1840s, when the German-born Prince Albert imported the tradition. It was the middle of the 17th century before tea became common in the UK. Potatoes, tobacco and chocolate didn’t come to the UK until the latter half of the 16th century.
Imagine you found yourself thrust back in time into your nation’s past, along with another time traveler. Your fellow time traveler tries to prevent a melding of cultures which resulted in the culture you know being formed. Would you assist them? If not, why would you do the same today?
If you think ‘they’ are diluting ‘our’ culture, what exactly is it that you want to protect? Which version of your nation’s culture is the pure version that you’re trying to uphold? If you object to parts of ‘their’ culture, do you object equally as strongly to similar practices in ‘our’ culture? If you object to halal slaughter of animals, do you object as strongly to abattoirs? If you’re outraged by Muslim paedophiles, are you as strongly outraged by the Catholic church’s systematic cover-up of abuse?