Here is the official Watchtower policy. The real reason is that they are afraid they might read something that might wake them up to what the Bible really teaches.
Watchtower 1984 5/1 31 Questions From Readers
Why
do Jehovah?s Witnesses decline to exchange their Bible study aids for the religious literature of people they meet?Jehovah?s Witnesses carry on their public ministry in obedience to divine instructions. Jesus said that during this "conclusion of the system of things," the "good news of the kingdom [must] be preached in all the inhabited earth for a witness to all the nations; and then the end will come." (Matthew 24:3, 14) So Witnesses do not go to people?s doors searching for truth or enlightenment. Rather, they already have devoted countless hours learning the truth from God?s Word and, having taken in the "good news," they are obediently going forth to share it.
Many people who believe that ?there is good in all religions? might consider it narrow-minded to think otherwise. (Contrast Jesus? view expressed at Matthew 7:13, 14, 21-23.) The Greek philosophers in ancient Athens encouraged such an "open-minded" attitude and enjoyed "telling something or listening to something new." (Acts 17:18-21) But when the apostle Paul appeared before them, it was not to swap philosophies or ideas. He used the occasion to present what he knew to be the truth, whether he was considered narrow-minded or not. While some of those Athenians mocked him, a number responded and became believers.?Acts 17:32-34; 2 Corinthians 6:14-18.
Paul obviously was aware of some Greek teachings, and he used such knowledge to give a most effective witness. (Acts 17:28) Similarly, Jehovah?s Witnesses are not ignorant of others? beliefs. They have gained considerable basic knowledge of the doctrinal beliefs of religions common in their area. Consideration to such teachings has been given in the book What Has Religion Done for Mankind? as well as numerous articles in The Watchtower and Awake! Such information on various religions is presented in the context of its contrast with accurate Biblical teachings.
God?s Word warns Christians that "Satan himself keeps transforming himself into an angel of light. It is therefore nothing great if his ministers also keep transforming themselves into ministers of righteousness. But their end shall be according to their works." (2 Corinthians 11:14, 15) Satan so successfully appeared as "an angel of light" that he was able to deceive even a perfect human, Eve. (1 Timothy 2:14) So it would be foolhardy, as well as a waste of valuable time, for Jehovah?s Witnesses to accept and expose themselves to false religious literature that is designed to deceive. They have no intention of falling into the sad course of the Jews, whom Paul said "exchanged the truth of God for the lie."?Romans 1:25, NW; Revised Standard Version.
Furthermore, some of the religious literature that people may urge Jehovah?s Witnesses to read is written by, or contains the thoughts of, individuals who have apostatized. True Christians are commanded to shun such apostates. (2 John 9-11; Titus 3:10, 11) Appropriately, then, The Watchtower of June 15, 1983, counseled:
"In the first century, Hymenaeus and Philetus turned apostate and tried to subvert the faith of others. God?s standard was: ?Shun such empty speeches that violate what is holy.? (2 Timothy 2:16-19) Christians holding to that standard would not have been interested in listening to apostates, nor in obtaining any poisonous writings that these might distribute ?for the sake of dishonest gain.? Why finance their wickedness by buying their literature? (Titus 1:11) As loyal Christians let us hold to God?s standards, feeding our minds on what is true and righteous, and holding appreciatively and loyally to the channel from which we first learned Bible truth.?Compare 1 Timothy 4:16."?Page 15.
Hence, it is out of wisdom and respect for God?s counsel that Jehovah?s Witnesses do not make a practice of exchanging valuable Bible study aids containing Scriptural truth for religious literature that disseminates error or apostate views.