No African-American students?

Schools in the 50s were under no obligations to accept students of color.

A school like the one in Dead Poets was also one built on legacy admissions so it isn't difficult to see why the student body would be entirely white.

Both.

Of course there were some well-off African-American families, but they weren't particularly encouraged to apply. And there were some scholarships, but that wasn't who got them.

Worth noting is that, into the period of the movie (and more so earlier), the big prep schools consciously kept down the number of Jewish students, many of whom could afford it, and were well qualified academically. The schools were intended for "people like us" (as an alumnus might put it).

The leading prep schools first began making an effort toward diversity in the mid- to late-sixties.

the movie is set in the late 50's, dude. educate yourself on the history of civil rights.

Well Tony, nobody wants a war. If we can't do business why we'll just shake hands and that'll be it!

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Also no Asians or Latinos. Elite schools like this were essential for the wealthy or upper middle class WASP crowd. Over time (and by 1959, when the film was set), Jews and Catholics managed to gain admittance (although I did no recall anyone in the film with a Jewish, Italian or Irish name). You really don't get more upper crust than someone named Knox Overstreet.

Both.