I have heard abour some customs from around the world that require one to eat or drink a local food or beverage when offered. The person offering the item is said to take offence if the item is not drank or eaten. How does one politely get around this. I do not drink and there are items I will not eat.
In Asia (speaking very generally) this normally means someone is hosting you. It could be a family member, friend, colleague, business partner etc, rather than a tourist. There is no way around it, you just have to eat it or you risk causing offence. Keep an open mind. Generally people won't offer something they think a foreigner won't like, but you can't be picky. I'm not a fan of durian, for example, but it would be rude to refuse.
I don't drink alcohol for religious reasons, and that is something that is respected.