The current global trade (non-software) relies on security provided by US Navy. Global Trade is not Free Trade! You need a security under-writer for it. I think Libertarians have a "blind-spot" there.
I'm not sure about that, unless you're conflating libertarians with anarcho-capitalists. Minarchist libertarians would actually consider that making free trade possible through military might is in the purview of the state.
If you're a Libertarian and you believe spurring on global trade strengthens the right to property and disrupts governments from legislating moral imperatives, then you might be a globalist. Being neutral to OK with globalism is not the same thing as being a globalist.
I would say yes, take away national governments and you empower multinationals to essentially turn the world into their corporate serfs, with the rule if law gone corporation's are free to impose their own rules without any vote by the people on the matter.
Aren't libertarians also globalists?