I think the difference between Wheaton's policy and the AEA policy is that Wheaton's primary purpose is a Christian education. Some of the JNV commentators asked how "Christian economics" differed from non-Christian economics. In so far as we're talking the direction of demand curves and so on, the answer would be not at all. But if we're talking about defining the institutional mission as promoting a Christian educational philosophy and ensuring that the faculty all buy in to it, support it, and are prepared to counsel students outside the classroom appropriately, then it seems to me that there is a large difference.
I teach at a secular, private school. I don't hide my faith (my office has icons, admittedly mixed in with folk religion artifacts from Guatemala and Mexico) but it would never occur to me to initiate a conversation about it with a student. That, presumably, is not what teaching at Wheaton is like (and perhaps PJ can enlighten us further - some Wheaton students, including a PJ fan, have comments on JNV's post).
The AEA, on the other hand, is engaging in a bit of mission creep when it expands its activities from economics to policing the content of job announcements. Moreover, the effect of the AEA's policy, if it were effective at deterring schools from requiring religious beliefs as a condition of employment, is to reduce the diversity of options available to students by making institutions more homogenous. The effect of Wheaton's criteria is to give a prospective economics student the choice of a Christian school or a secular one. (Some related thoughts are available in a recent working paper of mine on the issue of whether law schools constitute expressive associations independently from universities, available here.) That makes a difference in my view.
Update: There's more on this at Mirror of Justice.