The default view among Christians is that if unbelievers think better of Christians, they will be more likely to become believers themselves. It certainly sounds more plausible than the opposite formulation, that how they view us is irrelevant to their eventual decisions about Jesus Christ.
And yet I have to wonder, as the result of this is that Christians naturally gravitate to getting people to like us, or our churches, or at least not hate us or think us entirely unreasonable - rather to think better of Christ. - whether this does not miss the mark fairly thoroughly. CS Lewis wrote in several places about First and Second Things - that if we aim for the lower goal we get neither, yet if we aim for the main thing we get all the secondary gains thrown in. But seek first God's Kingdom, and his righteousness; and all these things will be given to you as well.
One possible response would be doing nothing but good works and holding camp meeting revivals. We scoff that this would of course be ridiculously ineffective. Yet this used to be the model for the early Wesleyans, and later the Salvation Army. Did that work?