I'm an American mathematician, and I've never experienced a situation where 0 being an element of the Naturals was called out. It's less ubiquitous than I'd like it to be, but at worst they're considered equally viable conventions of notation or else undecided.

I've always used N to indicate the naturals including 0, and that's what was taught to me in my foundations class.

The US is one of 3 countries on the planet that still stubbornly primarily uses imperial units. "The US doesn't do it that way" isn't a great argument for not adopting a standard.

I have yet to meet a single logician, american or otherwise, who would use the definition without 0.

That said, it seems to depend on the field. I think I've had this discussion with a friend working in analysis.

This isn't strictly true. I went to school for math in America, and I don't think I've ever encountered a zero-exclusive definition of the natural numbers.