The "rejectionists" al-Barak speaks of are Shiite Muslims, whom he considers "more dangerous than Jews and Christians." For al-Barak, being a nation "under God" means being a nation under his Sunni Muslim conception of God.
Considering the sectarian civil war that has been going on in Iraq, what would we tell the people of Iraq if they decided to adopt "one nation under God" as their national motto?
Does this suggest any reason that the phrase "one nation under God" should not be allowed as a wedge to suggest to religious authoritarians that we are a nation under their particular conception of "God?"
From Chapter 6 of The Authoritarians
One of the easiest mistakes to make when judging a threatening movement is to perceive it as being more unified and monolithic than it really is. So let’s do a little speculating here. Let’s suppose the Religious Right gains long-term control of the executive, legislative and judiciary branches of the federal government and accomplishes its common agenda ...And as James Madison put it (bold emphasis mine)
Would the victors then all clap each other on the back and live happily ever after in Taliban America? Maybe they would. But recalling what we know about the dominance drives and prejudices of Double Highs, wouldn’t a subsequent Catholic versus Protestant struggle for control be just as likely? Coalitions last only as long as the common enemy [e.g. godless "liberals" or S-Ps] does, and few things provoke animosity the way religious differences do among the very religious. And if the Protestants subdued the Catholics, would that be the end of religious warfare, or the beginning of the next round? After all, Baptists and Pentecostals don’t really like each other all that much.
The free men of America did not wait till usurped power had strengthened itself by exercise, and entangled the question in precedents. They saw all the consequences in the principle, and they avoided the consequences by denying the principle. We revere this lesson too much soon to forget it. Who does not see that the same authority which can establish Christianity, in exclusion of all other Religions, may establish with the same ease any particular sect of Christians, in exclusion of all other Sects.