Myers belongs to the Anabaptist Mennonite faith, which condemns the mixture of church and state. Anabaptist Mennonites are a Christian sect that "left Central Europe in late 1600 because of religious persecution for belief in the separation of church and state."
According to the Mennonite Confession of Faith, "[t]he primary allegiance of all Christians is to Christ’s kingdom, not the state or society. Because their citizenship is in heaven, Christians are called to resist the idolatrous temptation to give to the state the devotion that is owed to God."
Myers lost, in a ruling issued today by the 4th Circuit Court of Appeal, consisting of three separate opinions (one for the court and two concurring):
Myers v. Loudon County Public Schools
It's a 25-page opinion but the actual Establishment Clause analysis doesn't begin to be addressed until page 11. After the now-mandatory, selective discussion of the history of public religion in the U.S.
à la faux-historian William Rehnquist, the court determines finally, on page 21, that despite "undoubtedly ... contain[ing] a religious phrase," the Pledge is a patriotic exercise and not a religious one.
Pretty flimsy stuff, from the looks of it, at least in terms of controlling precedent from which to draw. The 4th Circuit even acknowledges this:
Although we are not bound by dicta or separate opinions of the Supreme Court, "observations by the Court, interpreting the First Amendment and clarifying the application of its Establishment Clause jurisprudence, constitute the sort of dicta that has considerable persuasive value in the inferior courts." ... Moreover, in the context of this case it is perhaps more noteworthy that, given the vast number of Establishment Clause cases to come before the Court, not one Justice has ever suggested that the Pledge is unconstitutional. In an area of law sometimes marked by befuddlement and lack of agreement, such unanimity is striking.
That's the 4th Circuit's emphasis.
Not exactly the finest example of compelling legal reasoning one might expect from this level of court.