That's a curiously passive idea about what happens if you do. Everyone has always been begging, borrowing, stealing, adopting and adapting anyway – and that way interesting new stuff gets invented. Culture isn't some static thing – it's more like a constant improvisation of certain themes, and it thrives on adoption and adaption.I never liked the idea that the way to get along is to blend all the cultures and races together so that everybody would be the same. How boring.
The danger is unlikely to be the mixing, but more the modern tendency to homogenize through instant communication and coordination and lowest-common denominator one-size-fits-all products – which tends to be expedient for marketing purposes, when everyone demands the same things to the same level of specs. (Makes it easy and practical to cater to, and then some get nauseatingly rich in the process.)