What does Romans 14:3 mean?

Paul has defined two different groups of Christians in the early church. In the context of actions not clearly labeled as sinful or righteous by Scripture, Paul considers those of "weak faith" in contrast to those who are more secure in their faith. Those in both groups were true believers in Jesus. The difference was found in their opinions about what Christians should be free to participate in versus what they should stay away from. In the previous verse, Paul identified an example: those who refuse to eat meat for religious reasons, being weak in faith. Those of stronger faith felt free to eat anything at all, because they were convinced that Christ has freed them from all the requirements of the law and they were fully accepted by God's grace through faith in Christ.

Paul, though, does not condemn the religious vegetarians for their opinion. Instead, he forbids both groups from despising or passing judgment on each other. God has welcomed all who are in Christ, whether they live in the full freedom of God's grace or not. As such, both groups should welcome each other.

This statement is a crucial part of the context of chapter 14. It coordinates with Paul's other remarks on Christian liberty (1 Corinthians 10:23–33; 1 Timothy 4:4). Those who feel free to partake in certain things should not look down on those who are not comfortable with that same activity. At the same time, those who feel a personal conviction about something ought not judge those who do not share their conviction.

In short, both sides need to respect and tolerate each other (Colossians 2:16–23).