In refusing to submit to a lawful, federal judicial order. According to Romans 13, arguably he did. I sent a little email to Joseph Farah along those lines and he published it in today's letters section of WND.
Unbiblical Founding Fathers
Judge Roy Moore's actions in disobeying a federal judicial order was, according to the Bible, sinful. Romans 13 demands submission to governing legal authorities. You and Moore are confused because you think that somehow if America's Founders did it (i.e., revolt), it must have been biblical. America's principle Founders (Washington, Adams, Jefferson, Madison and Franklin) – though they may be categorized as "Christians" in some broader, more liberal sense of the term – were not biblical, orthodox Christians. They were rationalists who took a cafeteria approach to the Bible and theological unitarians and universalists to boot.
Some of my previous analysis on this issue (Romans 13 and obedience to government) may not have been clear enough in that I didn't distinguish between obedience to government and submission to government. The Bible doesn't, I think, forbid civil disobedience (obviously if government commands you to disobey God or sin, a believer wouldn't have to comply). It does, however, demand you submit to the lawful authorities (whomever they may be), and accept the legal consequences of your disobedience -- even if it means getting thrown to the Lions or in Jesus' case, crucified. Revolt, as I read the text, is forbidden.
That's not just the way I interpret the Bible. It's also the way Calvin, Christian Tory ministers during the founding era, and virtually every Christian thinker until the 1600s interpreted the Bible and Romans 13. "The people," according to this traditional understanding of Scripture, have as much "right" to decide their leaders as they do to decide their parents.
The most I'd be willing to concede is Romans 13 and Titus iii can be explained away in context and don't stand in the way for a believer to support revolt. However, the Bible still nowhere authorizes revolt and the ideas contained in the Declaration of Independence, though obviously theistic, are nonetheless wholly alien to the Bible. As Robert Kraynak once put it: "[M]odern liberal democracy needs God, but God is not as liberal or as democratic as we would like Him to be."
More to the point on whether Roy Moore violated Romans 13, Justice Scalia, from his reasoning in this article (discussing the death penalty and conscience), agrees with my analysis. He would note if Moore had a problem following the ruling, he could have resigned his position. Scalia probably thinks Moore's actions in displaying his statue of the Ten Commandments were constitutional. But would also note the proper way to handle that is follow the legal process: If you don't like a lower federal court's ruling, appeal it to a higher court, eventually to the Supreme Court, and you may be able to get relief there. If the buck stops at a lower federal court that declares your display unconstitutional, Scalia would note a believer should either follow the order or resign.
Ultimately Moore was properly removed for his lawless actions.