You are falling for the false relationship between globalization (lowercase ‘g’) and being a Globalist (capitalized.) Globalization is a natural economic result of ease of trade and transfer of currency and goods/services. Globalization happens because transport is eased through technology.
Being a ‘Globalist’ however, is different, it is the belief that there should be an all inclusive overriding global authority on all issues (such as the UN.) This authority would override state sovereignty.
Globalization is good, Globalists are bad.