If you want to sell books produced in the UK in another country, especially if it is an important market, you tailor the content of the book to the market. Indeed, you do that wherever you want to sell them – just like any other product. I write cook books and the US market is essential because the masses of colour photography in such books is expensive and the US market is big and lucrative. Consequently, I tend to avoid including recipes with gooseberries, physalis, ice cream wafers, red, white or black currants, taramasalata or pickled beetroot, for example. I also tend to include more Italian, Chinese, Japanese and Latin American recipes than Indian ones in global cook books. (I even call them cook books rather than cookery books
).
In the case of the English-language teaching books and others, it's not simply a case of avoiding giving offence but of making the books attractive – and therefore saleable. Jolly little pigs, family dogs, mixed sex groups of young people sharing a house or drinking alcohol, families going to church on Sunday mornings, etc., while not necessarily offensive, are simply not attractive in some markets and there will be many other books to buy.
Don't let's fall into the trap of "It's the American Way so it must be the best". Just because something works in the culture of the UK doesn't mean it is right elsewhere.