When we have two thoughts that are mutually exclusive, our thinking is incongruent.  It is inconsistent.  We are having two thoughts, and those two thoughts cannot both be true.  An example would be believing that something is at once and in the same way both true and false.  That cannot happen.  Generally, the reason we are fooled by these thoughts is because they are not obvious at first, though it seems that we are aware of the problem at some level.

Part of our ongoing sanctification involves the Holy Spirit coming into our lives and purging out the lies.  When the lies go, all the incongruent thinking goes with it.

Incongruency Examples:

Christians who engage in sex outside of marriage or any other form of willful sin.  Justifying sin and walking with Christ are mutually exclusive. That doesn't mean that if you slip and fall into sin that you lose your salvation. The word, sin, means to either step or slip off of the Way that leads to the genuine and absolute fullness of Life. Continuing to ignore God's leading will sear your conscience and you will eventually create barriers between you and God. Christ came to remove those barriers. Entering into sin again and ignoring God's leading will rebuild those barriers.

Christians who believe that the Bible is the Word of God without error and also believe in Evolution.  Many Christians may be in this situation from simple lack of knowledge of the story of evolution and/or the Bible.  There is no way to reconcile the Bible to the story of evolution.  It is one or the other.

Christians who believe that the truth of the flood in the Bible and also believe that the Earth is older than the Bible says that it is and that the fossils are not evidence of the flood but rather evidence of millions of years of animals and plants.  It is one or the other since a flood of the nature that is described in the Bible would have destroyed any previous fossil evidence.

It is incongruent to believe that early humanity was primitive if you are a Christian.

It is incongruent to believe that there was death before sin if you are a Christian, since the wages of sin is death and death came into the world by sin.

It is inconguent thinking to be a Christian and yet try to fit in with the culture.  Whoever loves the culture, the world, is an enemy of God.

It is incongruent to have a theology that believes in salvation through the blood of Christ but also salvation depending on some kind of work or penance that you must do.

It is incongruent to believe that our righteousness is as filthy rags as the Bible says it is, and also believe that we Christians do works for the purpose of showing God how thankful we are for salvation.  Hint: The Book of Romans clearly tells us that works of righteousness are gifts from God that come by grace through faith and are the result of God doing His works through us.

It is incongruent to be a Christ-follower and also refuse to believe in a real Adam and Eve.  These claims are not based on either science or the Bible.

It is incongruent to place the claims of the most vocal scientists above what God says and, at the same time, claim to be a Christ-follower.

The assumptions of rationalism and Naturalism are so ingrained in us by the culture that it makes it easy for us to be tricked by naturalistic explanations.  It is incongruent thinking to try to interpret the Bible by the power of the fallen human mind as opposed to coming in humility before God and asking for revelation.

It is incongruent to believe that God is almighty and all-wise and would have all men to be saved (all true and clearly stated in Scripture) and also believe in some theology that has God losing most people to hell without any restoration at any time.  This is especially true given the fact that the Bible says such things as, "As in Adam all die, so in Christ shall all be made alive."