Galatians 2:21 I do not frustrate the grace of God: for if righteousness come by the law, then Christ is dead in vain.
In reading this verse, I assume that most Orthodox preachers conclude that the "law" referenced is specifically the Law of Moses and not rule keeping in general. I say that because Orthodoxy most definitely teaches a righteousness based on obedience to rules and the following of procedures. Various churches define the rules differently and use different terms to indicate the law relative to Christianity: plan of salvation, Gospel message, Law of Christ, etc.; but, in a practical sense, all Orthodox Christianity is essentially the same. Obey the requirements and achieve righteousness. Disobey and suffer the consequences. The doctrinal position of Orthodoxy in relation to right standing before God is not significantly different from that under Moses. The rules are different; but righteousness is till sought by obedience, which is an effort of human commitment and will power. It is hard to see why this very similar methodology in the NT would lead to better results than in the OT.
The church apparently thinks that because Jesus made a more perfect sacrifice that righteousness by obedience to NT law becomes easier or better in some way from righteousness by obedience under the Law of Moses. Of course, their longstanding understanding that very few will actually achieve righteousness through Christ, in reality, denies any difference in effectiveness.
One can obviously read Galatians 2:21 and draw the conclusion that it refers only to the Law of Moses and not rule keeping in general. However, that is not the only possible conclusion. When we consider the broader issues, like what is God's stated desire about the scope and effectiveness of redemption and the history of law keeping as a route to righteousness, more specifically the example of OT Israel, we can justifiably draw a different conclusion. What Paul condemns as negating the work of Christ is not just Mosaic obedience but obedience in general. Grace is not activated by reliance on obedience but rejected or denied by it.