Like the topic on women, this mostly focuses on psychology, but the bigotry applies to other fields as well.

Jewish:
A study of discrimination at elite universities -- Harvard, Yale, and Princeton -- in the '60s found blatant antisemitism, with admissions attempting to keep the "Jewish invasion" under control. Accepted Jews were not allowed to join fraternities or social clubs. "If Jews get in, they would ruin Princeton" (Karabel, 2005, pg. 75)
Many universities had policy that prevented Jews from teaching.
Isadore Krechevsky had to change his name after earning his PhD to David Krech in order to find a job.
David Bakanovsky in the 40s at the University of Iowa was told that he'd never obtain an academic position due to "several faculty members who believed that Iowa had graduated too many Jewish students" (Weizmann & Weiss, 2005, pg 317).
Harry Israel, not even Jewish, was told "It makes no different about his qualification. [The university] can't take a man with that name." (Leroy & Kimble, 2003, pg 280).
Abraham Maslow was told to change his name to something "less obviously Jewish" in order to obtain an academic job.
Daniel Harris, with a PhD from Columbia University in 1931, was told he could not be a research assistant because he was Jewish and that he "shouldn't be too hopeful about finding an academic career" (Winston, 1996, pg 33).

African American:
In the 30s and 40s, many colleges did not allow black students to live on campus.
Francis Sumner, the first black student to earn a PhD in psychology, was given a separate table in the dining hall due to his race.
From 1920 to 1966, the ten most prestigious psychology departments in the U.S. combined awarded only 8 doctorates to blacks, out of the total 3,700 awarded.
Cornell refused to accept Kenneth Clark due to his race, telling him that PhD candidates have trk too closely together for a black person to join in.
His wife, Mamie Clark, could only find work analyzing data (Bachelor-level or under work, even though she had a PhD).
In the 40s, they performed the research that the Supreme Court used to end racial segregation in public schools (considered the most important SC decision of the 20th century), and Kenneth became the first black president of the APA. Yet both had huge trouble finding employment due to racism.

Both blacks and hispanics are underrepresented in acceptance into graduate programs, hired as academic professors, or memberships into academic institutions.

Whites make up 65% of the population, yet earn 80% of doctoral degrees in psychology.
The only minority that earns a degree at a level equivalent to their population is Asian Americans.