It depends on what you're doing, though. If you're helping people fill out documents (even non-government documents), then you really need to match the country

It depends on what you're doing, though. If you're helping people fill out documents (even non-government documents), then you really need to match the country standard. Localization is important; some countries outright require it if you're going to do business within their borders. But even where it's not required, you will lose customers if your website/application/product feels "foreign". I'm not sure date ordering is a big enough deal to trigger that feeling in anyone, but unless it's a huge burden to format things the way people expect, I would do so for the UX benefits.