What does 1 Corinthians 10:29 mean?
This clarifies what Paul has written in the previous verse. He said that if Christians were told the food being served at a dinner party had been offered to idols, they should not eat it for the sake of conscience. It's important to remember that the meat, itself, is not taboo, and the idols are not actual gods (1 Corinthians 8:4–6). It's not necessary for a person to investigate their food for spiritual connections (1 Corinthians 10:25–27). At the same time, anything can become a sin when it's used in violation of a person's conscience (Romans 14:23; 1 Corinthians 8:7).This means the "conscience" in question for this principle is not that of the individual Christian. It is that of others: either the person who tells them the meat is sacrificial, or for the sake of the "weaker" Christians who may be present. Skipping the idol food is best, to avoid leading another person to believe that Christians approve in any way of the worship of idols.
Paul's next two questions, in this and the following verse, can be confusing when taken outside the flow of the text. Earlier, Paul noted that he was speaking as though to reasonable people (1 Corinthians 10:15). That included asking questions to which the answers are common-sense and obvious (1 Corinthians 10:16–18).
Taking all of what's written here into account, these verses are re-statements of Paul's earlier teaching that there is nothing wrong with the food itself. They also support his view that God-guided conscience, not shallow legalism, shows us the boundaries of sin. Paul may be suggesting that Christians should allow another person's conscience to determine how they will exercise their freedom in Christ. The other person's conscience, however, doesn't get to set boundaries on what Paul is free to say or do in other circumstances. In other words, they have the freedom to eat idol food, but they should restrict their own freedom for the sake of another person's conscience.
Another perspective is to refer to prior comments about eating meat with a clear conscience when one doesn't know whether the food is idol food. Paul is suggesting that another person's conscience—about eating idol food in ignorance—should not be the thing that determines his own Christian liberty.