However, later on the same web page they say "Listings that indicate discrimination on the basis of religion are not permitted even if the employer is eligible to discriminate on the basis of religion under Sec. 703(e) of the Civil Rights Act of 1964." And Wheaton does fall in that category; we are legally allowed to impose religious standards as conditions of employment. Our job advertisement contains an explicit statement about our faith position and the requirement that employees adhere to that commitment.
So, we have an interesting problem. Several members of our department belong to the AEA. We would like to fulfill our professional obligations,and would also like to make known our job opening to as wide an audience as possible. But evidently the AEA regards colleges that require a religious commitment "beyond the pale" in terms of acceptable conditions of employment.
I would argue that private institutions, like Wheaton College,which wish to organize their educational mission around a particular world view (in our case the Christian faith) should have every right to do so. I find it interesting that the American Economics Association either believes such discrimination immoral, or that it leads to the production of bad economics. I suspect it is the former. But I question whether it is wise to rule out commitments to eternal verities as an appropriate criteria for organizing one's life and one's association with others. We live in a world with numerous claims about what constitutes truth. A society that allows individuals and organizations to make particular truth claims and to organize themselves around such claims is a much healthier (and diverse) one than a society that rules out such claims as organizing principles. I would much prefer a world where private organizations could choose their belief structure and then be allowed to impose those on anyone who chose to join them.