High school education in the US typically requires a 1
semester economics course, at most. A one semester or one year government/civics course. Two years of history (US and World, the latter typically being very eurocentric). In the sciences, college bound students will have taken (usually) one year each of biology, chemistry and physics. On the math front they'll have gone through trigonometry, perhaps pre-calculus. For foreign languages they'll have usually taken two or three years of some language (almost universally available: French, Spanish; common: German; some regions or schools will have more options available). For literature (also known as language arts or English) they'll usually have taken three or four years. The first is often a refresher on composition, with reading really being intended only to provide material for discussion and writing assignments. The second and third courses are often region/time specific (American Lit, British Lit, World Lit from 300AD-800AD), the fourth (again, for college bound students) will involve more complex novels and writing assignments.
Knowledge of specific economists is not the norm in the basic college prep curriculum in the US. Students in the IB program (relatively rare, available in major cities so the majority don't have the option) or the AP program will have studied the subjects to a greater depth. At least equivalent to freshman/sophomore college courses in the subject.
For a bachelors degree the students will apply to schools and get in based on: GPA, SAT/ACT scores, extracurricular activities, interview (not used for the average university), and essays. Some schools put all freshmen into the same pot and require them to apply to their major after their freshman year. In that case, it'd be similar to your "Don't know Keynes? Probably won't get an offer." situation. However, that's also not the norm. And once at the school the students can usually change major with ease.