Course catalogs are widely available on the internet. Usually, the graduation requirements are included in the catalog. I'm not aware of any major universities that compel undergraduates to take a research method class as a condition of graduation, though I wouldn't rule out a change since the last time I looked at a catalog. I'm aware of plenty that have or had compulsory philosophy or religion courses within our lifetimes.
In general, any compulsory research methods classes are taught at the graduate level, which most people don't reach. In practice, what you have to know in order to function in many of the resulting professions is to stay current on generally accepted best practices for one's area of work - which is not necessarily the same as distinguishing good research from bad.
This has little to do with whether or not you value xG - a treatment of its merits and flaws are well beyond the scope of any conversation here. But if you want to know why people broadly believe bogus research on vaccines, I'd posit that there'd be less of that if we actually taught people to discern good research from bad.