I think Christians are sometimes that way around unbelievers. They appear as though they are avoiding all contact with them. I can understand not wanting to be influenced in a bad way. But how about influencing others in a good way?
Jesus said that as Christians, we are to be salt and light. In Jesus' day, salt was used as a preservative. It was rubbed into meat to stop the rotting process. So as salt in a culture, Christians are to stop the spread of corruption. But another thing salt does is stimulate thirst. So we are to stop the spread of corruption and stimulate a thirst for God in others.
In addition to being salt, Christians are to be light, which means that we are to proclaim the gospel and do good works. Jesus said, "Let your light so shine before men, that they may see your good works and glorify your Father in heaven" (Matthew 5:16).
We are called to be salt and light—to live a godly life. It is God's job to identify the fake Christians, to determine the true from the false.
God has planted us as believers in this world. He has put His people in the culture to influence it, to make a difference. God is not calling us as believers to isolate, but to infiltrate.