Perhaps the biggest problem with the TE/EC model is that it rejects the historicity of Adam and Eve. This is a problem because the Scriptures seem to present Adam and Eve as actual persons. This can be seen, for example, in the genealogies of Jesus Christ that appear in the Gospels of Matthew and Luke. Furthermore, in I Corinthians 15:21, the Apostle Paul tells us that "since death came through a man [Adam], the resurrection of the dead comes also through a man [Christ]." He goes on in the following verses to develop this contrast between Adam and Christ. However, if Adam did not really exist, Paul's analogy would break down. One could argue, I suppose, that Paul genuinely believed that Adam was a real person, but was mistaken. However, such an argument would undermine any belief in the trustworthiness of the Scriptures, which is an essential element of Christian orthodoxy. In his article, Luskin notes that the rejection of Adam and Eve's historicity by advocates of the TE/EC model is based on the idea that human genetic diversity cannot be explained if we are the descendants of a single human pair. However, as he points out, research by several scholars, including biologist Ann Gauger and computational biologist S. Joshua Swimidass, has shown that human genetic diversity is not incompatible with the idea of a single pair of human ancestors.
As for the Homo divinus model, it has the advantage of treating Adam and Eve as actual persons. So, in a sense, it is less problematic than the TE/EC model for Christian orthodoxy. However, it presents a different challenge to orthodox Christian belief--namely, it rejects the idea that Adam and Eve were created directly by God, which would appear to be what is taught in the first and second chapters of Genesis. I suppose that one could argue that the language in Genesis about God creating Adam from the dust of the earth and breathing the breathe of life into him is meant to be taken symbolically. However, while I do not pretend to be an expert on ancient Hebrew, it would appear that the language in Genesis is meant to be taken more-or-less literally. Luskin notes some other reasons why the Homo divinus model may be theologically problematic:
In proposing an Adam and Eve that are in no way biologically connected to the rest of the human race...this model may not satisfy Old Testament doctrines about Adam and Eve somehow transferring the "image of God" to the rest of humanity, nor New Testament doctrines Adam's sin and death somehow spreading through all humanity...
In short, like the TE/EC model, the Homo divinus model would appear to require us to abandon some elements of orthodox Christian belief.
In addition to the TE/EC and Homo divinus model, there are two other models--the Genealogical Adam and Eve (GAE) model and the Homo heidelbergensis model--which assume that at least part of humanity evolved rather than was directly created. These models are perhaps somewhat less problematic theologically than the TE/EC and Homo divinus models, but Luskin rightly points out--in my opinion, at least--that they may not be without their own theological problems.
Nonetheless, in arguing that the TE/EC and Homo divinus models (and possibly the GAE and Homo heidelbergensis models) are inconsistent with Christian orthodoxy, I am not necessarily arguing that those who hold to these models are not genuine Christians. It is possible that those who advocate these models otherwise hold to orthodox Christian doctrine--even if certain aspects of that doctrine are arguably incompatible with the models of human origins they advocate. In such a case, they would be merely guilty of a sort of philosophical inconsistency. On the other hand, to the extent that their advocacy of either of these two models causes them to abandon other key Christian teachings, then I would question their orthodoxy.
In short, while there are certainly a number of options for Christian believers to chose from in trying to reconcile faith and science, it seems--to me, at least--that some of these options are more compatible with genuine Christian faith than others.
Image: "Adam and Eve" by Hans Holbein, from Wikimedia Commons