The reasoning should be thus:

1. The wearing of a head-scarf is an outward and visible sign that the wearer takes her Islamic belief seriously. Anyone who identifies himself as a Muslim, and who then gives further proof that such identification is not merely a convenience, a matter of filial piety, or a case of a Muslim-for-identification-purposes-only Muslim, but of someone who takes the texts and tenets of Islam seriously, should be held to those texts, those tenets.

2. Anyone who takes to heart the texts, tenets, attitudes of islam - which in spirit and letter flatly contradict the principles of Infidel nation-states, and especially those advanced Western states that clearly are most solicitous of individual rights, and of the equality of men and women -- cannot conceivably do justice, that is do justice according to the principles of an Infidel nation-state. Such people are disqualified, by their beliefs -- which can be discovered by questioning them at length, offering them hypotheticals to be answered -- from being judges.

3. I would go farther. No Believing Muslim, no one who takes seriously his faith in Islam and therefore is committed to a view of the world in which the principles, say, of the American Constitution, wherever they clash -- and they clash everywhere -- with the Shari'a, must yield, at least in the court of that Muslim's mind -- can dispense justice, or even be part of the justice system.

4. Those who wish to be admitted to the Bar in the United States, state by state, are required to take an examination that includes Constitutional Law. But such an examination is not enough; they must swear to uphold the Constitution and mean it. But how can they mean it, if they are true to Islam, a collectivist faith that demands loyalty only to Islam and its principles, and to fellow members of the Umma? One can pretend this is not so. One can continue, in order to avoid controversy, the clash, the fatal contradiction, between the principles of the American Constitution, and the unwritten British Constitution, and the constitutions of all advanced Western states, on the one hand, and the Shari'a on the other. Or one can forthrightly examine those contradictions, and the need not to admit either to the Bar, or to the state administration of justice, those who cannot wholeheartedly support, and support against the teachings of the Qur'an, Hadith, and Sira, the principles of the Infidel nation-state in which Muslims have been allowed to settle, and where they may geographically locate themselves, but mentally, they are in quite a different place, and will continue to remain so, as long as they take their Islam seriously.

This understanding of things, unpleasant as it is, has one virtue: it happens to be true.