The noetic effect of sin is the effect upon the mind. The Greek word for "mind" is "nous." Therefore, "noetic" deals with the mind, or the rational aspect of the person. This effect means that our reasoning abilities are no longer pure and proper all the time. But, it does not mean we will always reason improperly. We can think rationally, use mathematics, make proper judgments, etc. But, as is obvious, there are many false religions in the world that are believed and defended intellectually. So, the noetic effect of sin upon the mind most assuredly manifests itself in the belief of false gods, false Christ, false gospels, etc.
When sin entered the world through Adam (Romans 5:12), our bodies began to decay. Our emotions were affected. And, our minds were corrupted. This is why we have so many different religions and, even within Christianity, we have so many different denominations. Our divisions the result of spiritual blindness and, ultimately, irrationality.
Does the noetic effect mean that people are completely incapable of understanding spiritual things? Some say yes, and others say no. There is a difference between understanding and accepting. Many nonbelievers can understand doctrinal issues of Scripture but will not believe them. So, there is a difference between ascentia (intellectual acknowledgment) and fiducia (faithful trust). So, on the one hand, those who are not regenerate can understand spiritual things but they cannot accept them and this seems to be the case as described in the Bible.
1 Corinthians 2:14, "But a natural man does not accept the things of the Spirit of God, for they are foolishness to him; and he cannot understand them, because they are spiritually appraised."
The fact remains that we are made in the image of God (Genesis 1:26). We can recognize certain logical absolutes such as the laws of logic and use them in debates. In fact, Christians have developed various logical proofs for God's existence using logic, evidence, and Scripture. But, they are resisted and denied by those who are outside of the faith. So, we could say that proof is different than persuasion and, since a person is unregenerate, he cannot be persuaded. Therefore, the noetic effect of sin will manifest, and unbelievers will use their minds to deny God's truth and remain in their sin.