A key in understanding how this chapter relates to us is in bearing in mind God's purpose in this destruction - the elimination of sin. The people groups being driven out were not simply followers of a different faith, though worshipping false gods in any form is blasphemous and offensive to the one and only Creator of the universe. But these people groups worshipped in ceremonies that celebrated the most vile sinful practices as part of their worship. Their entire culture centered around practices that were not only forbidden, but were an abomination in the eyes of God.
God calls us to this same level of annihilation of sin within our own lives. The picture of the Israelites' conquest is one that we replay in the spiritual realm when we follow Christ - we are to utterly destroy our own sinful nature through the power of the Holy Spirit so that we might enjoy the life Christ promised us.
Too often, I'm tempted to think I don't need to utterly destroy the sin. Can't I keep just this one little thing? It's not really so very bad, is it? It's definitely not as bad as what >>>> has going on . . . .
But God has made it so clear to me over the years that one little sin is like a cockroach...allow it to live and you will have a swarm before you know it. (sorry, gross - I know. But so is sin.) And my job is not to destroy the sin in someone else's life, or even to usurp the role of the Holy Spirit in trying to convict them of sin in their life. I have my hands quite full driving out the mess in my own heart.
God told Cain, "Sin is crouching at your door; it desires to have you, but you must rule over it."
In the New Testament, Paul warned the church at Colossae, "Put to death, therefore, whatever belongs to your earthly nature: sexual immorality, impurity, lust, evil desires and greed, which is idolatry." (Colossians 3:5)