The principal argument is that Sandra Day OConnors concurring opinion in Mitchell v. Helms is controlling in these cases: government cant directly aid religion or even "endorse" religion, and permitting government contractors to take religious considerations into account in hiring allegedly does both.
My first response is that predicting how Sandra Day OConnor will vote from one case to the next is an exercise in futility. She is above all dependent upon the context, which varies from one case to the next. The authors of the piece, at least one of whom is a long-time opponent of the "charitable choice" (the Clinton-era forerunner to the faith-based initiative), imply that faith-based organizations will always engage in invidious religious discrimination as opposed to merely mission-sensitive hiring, while "the facts on the ground," as they say, suggest otherwise. Most groups want simply to hire people who support their mission, which is a far cry from hiring, say, only Baptists or Catholics. While I dont happen to think that the this distinction is material, it could well matter in securing OConnors vote.
The authors also write as if the only religious freedom at stake here is that of potential employees. I would argue that, at the very least, we have to balance the freedom of potential employees and the freedom of those who comprise the organization. This sort of balancing is for the most part better left to legislators than to courts, though Im aware that mine (unfortunately) is a minority opinion.
In short, I dont find the arugments in the column all that persuasive.