First of all, “not being Catholic” and being an “unbeliever” are by no means synonomous. All Christians, for example, who belong to denominations other than Catholic are “non-Catholic,” but they’re still believers in the same Christian Scriptures and creed. Similarly, members of other religions like Judaism or Islam or Hinduism also believe in God. So you could — and hopefully you do — have some friends who are Protestant Christians or Jews or Muslims. We now live in the same neighborhoods, go to the same schools, and it’s good that we become friends, learn about each other’s faith, and treat each other with respect.
Who, then, was Paul talking about in the verse you cite (2 Corinthians 6:14)? His image of “yoked” refers to how it’s not helpful to yoke together two different animals — such as an ox and an ass — in order to get where you want to go. They’ll pull unevenly and maybe even in different directions. Paul’s point: The Corinthian Christians had many temptations all around them. They likely had friends who were not believers — pagans — and who expected them to keep living as they always had before they became part of the Church. In other words, they would be pulling them in a different direction and make it harder for them to live by the teachings of Jesus.
At the same time, we should note that Paul gives a different answer to the question of association with unbelievers in other places in his letters. At times he acknowledges — and condones — that believers are married to unbelievers (1 Corinthians 7:12-16). In 2 Corinthians 6:14 the general point is about the importance of human responsibility. We are obligated to honor our relationship with God by examining all other associations in light of that central relationship (with God). Any compromise of our relationship with God — speaking and acting in ways inconsistent with God’s own Spirit dwelling within us — is inappropriate.
from Fr. Tom Ryan, CSP, and the Busted Halo Question Box