ElectricThundah-
The people whom we are warned not to associate with are not people 'of the world'. They're people who claim to be fellow Christians, but at the same time are attempting to lead others astray through their actions:
I have written you in my letter not to associate with sexually immoral people - not at all meaning the people of this world who are immoral, or the greedy and swindlers, or idolaters. In that case you would have to leave this world. But now I am writing you that you must not associate with anyone who calls himself a brother but is sexually immoral or greedy, an idolater or a slanderer, a drunkard or a swindler. With such a man do not even eat.
What business is it of mine to judge those outside the church? Are you not to judge those inside? God will judge those outside. (I Corinthians 5:9-13a,NIV)
What those who are nonbelievers do is between them and God himself. Our responsibility is to live our own lives in such a manner that those who are nonbelievers will be drawn to it, seeing it as more desirable than the lifestyle which they now practise.
And that does not occur through our 'hitting them over the head' with our religious beliefs. It occurs through our own words and actions having as their source the motivations which God himself wants to be our new nature:
So I say, live by the Spirit, and you will not gratify the desires of the sinful nature. For the sinful nature desires what is contrary to the Spirit, and the Spirit what is contrary to the sinful nature. They are in conflict with each other, so that you do not do what you want. But if you are led by the Spirit, you are not under law.
The acts of the sinful nature are obvious: sexual immorality, impurity and debauchery; idolatry and witchcraft; hatred, discord, jealousy, fits of rage, selfish ambition, dissensions, factions and envy; drunkenness, orgies, and the like. I warn you, as I did before, that those who live like this will not inherit the kingdom of God.
But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, gentleness and self-control. Against such things there is no law. Those who belong to Christ Jesus have crucified the sinful nature with its passions and desires. Since we live by the Spirit, let us keep in step with the Spirit. Let us not become conceited, provoking and envying each other. (Galatians 5:16-26,NIV)
Note that many of the 'acts of the sinful nature' aren't actions in-and-of themselves. Instead, they're the underlying motivations which eventually culminate in the commission of sinful acts. Motivations such as hatred, jealousy, and dissensions can't lead to the performance of righteous acts anymore than a poisoned tree can yield good fruit. And this includes even those actions which some who claim to be religious would attempt to have us accept as God-willed.
It is when our words and actions have as their impetus those motivations listed as 'the fruit of the Spirit', and only then, that those words and actions have assurance of conforming to what God wants of us. It's not enough for us to do the right things; we must also do them for the right reasons. And the right reasons are the motivations listed as 'the fruit of the Spirit'. Their supreme importance to properly living a Christlike life is underscored by the words which immediately follow them: "Against such things there is no law."
And it is also when the motivations listed as 'the fruit of the Spirit' are the impetus for what we say and do that we attract even nonbelievers to us. Many of them associate Christianity with judgementalism, legalism, and even elitism over anyone who isn't also a Christian. But when instead they encounter Christians who exhibit 'the fruit of the Spirit' they are pleasantly surprised, as well as drawn to those motivations.