No, that is the same as apostasy from the religion. If religion says that X is just, and the laws are made that say Y is how you rule, then you do what the religion says, or you don't have the religion.
If a judge takes an oath to defend and support the Consitutution of the United States, and a law is enacted which is not in conflict with the Constitution, but is in conflict with his religion, he has no choice but to find the law constitutional. By negating the law, he would be acting not as a judge, but as a legislator, something almost all of us here on FR are vehemently against. That is why he must recuse himself in any case involving a conflict of interest. His religious beliefs would be a conflict of interest if it differed from a law that was otherwise constitutional.
Your secularism seems to say that whenever a particular view is traced to a religion -- e.g. a judge rules against contraception and is Catholic, -- that religious affiliation taints the decision rendering it invalid. I say, the decision may, of course, be badly argued or incorrectly arrived at, but the very fact that the judge's worldview comes form a particular religion is in no way a disqualifier.
Again, it would only be a disqualifier if the judge fails to do his duties as he took an oath to do. Let's say for example that the judge is a circuit court judge (appeals court). As such, if a case involving settled law is brought, he has a duty to either adjudicate in favor of the law, or recuse himself (step down in the case) if his religious beliefs conflict with the law. If he instead rules against the law, then he should be removed from the bench because he has violated the Constitution, the ultimate law of the land.
Obviously, as a Supreme Court justice he has much more latitude, because the USSC is the ultimate arbiter. USSC decisions can be reversed by the USSC or by a constitutional amendment.
Obviously, the presumption is that the judge attempts to do his job as defined by the Constitution and within the jurisdictional scope, nearly all the time, or else he simply won't be a judge for very long.
However, even though a judge, he does not cease to be human. If a conflict exists between the law of the land and the moral law, the judge must stick with the moral law and effect a positive change until such time as the gavel it pried from his dead cold hand. Resigning his position without a fight would be cowardly.