Not sure about the exact benefits/costs of globalization. It's already happened at high level business, trickling down into everyday business, largely driven by the United States policy makers. We've set the rules for globalization generally. Cat's out of the bag. Globalization will continue, whether the UK or the US or anyone else wants to or not. China's carving up Africa and Southeast Asia, and have been for awhile. Now they're moving into the Middle East and Eastern Europe.
The question we face isn't a choice between nationalism vs. globalism. Given that other world nations now have the ability to project power globally (namely China and Russia), the question is: Who do we want to lead the process of globalization?
I, for one, really hope that the US does, with EU and UK running 2nd fiddle. We should all fear a world where China makes the rules for global interaction. If we retreat from the position of international leader (which seems to be what nationalist effectively would get), that China takes up the pole position very shortly.
So, yes, globalization may cost us some jobs in the near term, may mean we need to let more people in, and may mean our American culture is going to evolve (which it always has - "American values" now are quite different from the Founding Fathers, et al) - but if we're not leading the global effort, China will. And that will cost America a lot more.