The Templeton foundation praised Abdullah II for building on "the power of principled pluralism."
Catholic officials required the retired archbishop to stop ministry activities. McCarrick maintained his innocence.
The "bold, unapologetic women" will share the second most important position in the 1.4 million–member denomination for two years.
The American Academy of Religion is committed to helping its members face an uncertain field, the leaders said.
Wingeier-Rayo is a fourth-generation missionary, having spent 15 years in Cuba, Mexico, Nicaragua, and the Rio Grande Valley.
The school's board of directors praised her “exceptional background in pedagogy.”
The scholar of religion and culture will become president in September.