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When one sins against another believer, he brings shame upon himself. When one sins against an unbeliever, he shames both himself and God.
When one commits a transgression against another Christian, one brings shame upon themselves. When one commits a transgression upon an unbeliever, they not only bring shame upon themselves, they bring shame upon Jesus.
I wasn't born a believer, but I was raised by believing parents. I started going to worship services before I knew what it was. The members of that little church were ordinary everyday people. The way they lived didn't cause me to believe or disbelieve the gospel of Jesus Christ. It was the gospel I had trouble with. It sounded like a fairy tale. Until it didn't. By then I was a fully grown man.
I don't believe the lifestyle of a believer can draw people to or deter people from coming to the Lord. I don't believe the hypocritical behavior of church members can keep a person from being born again when the Spirit of God sets His sights on that person. I think some of us give ourselves too much credit for too many things. No one comes to the Lord in Spirit and in truth because of how other people live their lives. It makes for a good sounding excuse to blame believers for you stiff arming God but that's all I think it is.
The biggest issue for me is how well it plays with the church. Some call it a circular firing squad. Unbelievers play christians against each other and many in the church seem to like it.
You must be born again to see the kingdom of God (John 3). You don't get born of the Spirit of your own accord. Nobody's lifestyle can prevail against the building of the church.
I'm not saying a believer's way of life doesn't matter; everybody's manner of living, believer or not, is important. I'm saying it doesn't keep people from being saved..
"How important is Christian conduct to how the unbelieving world sees Christ?"
When Jesus was here in person he was rejected by the world. The prophets had prophesied about him for hundreds of years, songs had been written about him, etc. Then he showed up, did all sorts of miracles, even raising the dead back to life, and he was rejected as the Christ, called names, and said to be a demon.
Was it his followers' conduct that caused the people to not believe in him? No! They didn't have the "grace" to believe. The people who followed him didn't do so because they believed the gospel. It was for other reasons. The disciples took turns asking him for a special place in his administration when he assumed the power he was to come into. They were clear examples of how his followers thought of him.
The Day of Pentecost describes the change that occurred when people began to believe the gospel when it is proclaimed. They received the Spirit of God (were born again) Acts 2. The Spirit is given by the grace of God, not by unbelievers observing the way believers live.
I say these things because the gospel has been contaminated with this kind of teaching for far far too long! It doesn't take diluting the good news with religious debris (chaff instead of wheat) to get believers to consider our ways (Hag 1:5, Heb 13:7). It is the truth that sets us free (John 8:32). So you have to read the scriptures with understanding, or listen to those who teach the truth.