It is not for your righteousness or for the uprightness of your heart that you are going to possess their land, but it is because of the wickedness of these nations that the Lord your God is driving them out before you, in order to confirm the oath which the Lord swore to your fathers, to Abraham, Isaac and Jacob (Deut 9:5).
If we employ a standard, time-honored exegesis of the above we may understand that Israel is the Church and the “land” is heaven. So, the Church does not go to heaven in light of their own righteousness, but rather because God made an oath to the patriarchs and is intent on keeping it.
Compare this with how Catholics think they make it into heaven:
[I]n infused righteousness God through Christ helps us to clean our dirty robe. This needs our cooperation and it is an on-going process. Our dirty robe is first washed clean through (Sacrament of) Baptism. Whenever we make it dirty again through sinning, God through Christ helps us to clean it through (Sacrament of) Reconciliation. When we die with our robe still stained with venial sin then purgatory will cleanse it.
Catholicism teaches that someone has to be literally righteous to enter the Promise Land. Ironically, this directly contradicts what the Scripture actually says.
Orthodox Christian Theology 
Doesn’t the example of Achan show that while Israel was unconditionally elected to take possession of the land, within the context of those who are engaged in that endeavor, obedience was necessary?
Not exactly. Obedience is not the condition that allows the Jews to enter the promised land, or it would make Deut 9:5. However, obedience does keep the Jews in the promised land and disobedience kicks them out. Hence, no Christian will live a life disobedient to God.
“Obedience is not the condition that allows the Jews to enter the promised land, ”
Right, and Catholics would say that it is not mere obedience which allows one to inherit eternal life. What’s the problem?
Revisit the actual article that you are replying to and read what Catholics write about infused righteousness. Catholic doctrine teaches that in order to stand before God, one has to literally be righteous. The righteousness must dwell in them, and any taint of sin must be purged before one enters the promised land.
Obviously, this cannot be true and have Deut 9:5 make sense.
However, when we are in glory (i.e. dead and in heaven) we will no longer have “the flesh,” so we will have no taint of sin and unlike Achen, can never lose the promise.
What you are trying to do is pit Moses against Moses, saying we need obedience and faith to enter the promised land. However, that is not what the Scripture says, you are adding to it. Faith gets you in, not obedience. The faithful will be obedient, don’t get me wrong, but the obedience is not a precondition. Rather, it is an inevitable consequence of faith.
Further, all Christians must come to grips with the fact that we in our bodies do not offer God perfect obedience. Look at the Law, how far short of the Law do you fall every day? H0w often do you covet? How often fo you love GOd with your whole heart, mind, and soul?
So, faith brings about the forgiveness of sins which makes all the faithful right before God, because their incomplete obedience is made acceptable. Incomplete obedience can be forgiven, nailed to the cross. Those without faith must pay the enalty for their disobedience.
In heaven, some men like David will have lived lives with frequent disobedience, even on their death beds. Others, like Paul and Job, will have lived lives almost like angels. All these men will appear completely righteous before God because of what Christ did on the cross.