Someone asked me recently what the Bible says about a person who claims to be a Christian, and yet continues to live in sin. My answer, pretty much off the top of my head is as follows:
Matthew 7:15-23 is very clear. The fruit of conversion will be evident. The person who merely claims to know Jesus, but does not bear the fruit of a changed life is simply fooling themselves. They are inwardly wolves, not sheep. v 18 says that a good tree cannot bear bad fruit, nor can a bad tree produce good fruit. The fruit of the life will give evidence to whether or not the heart has been changed by grace
Romans 8:5-8 makes clear that those who are still "in the flesh" cannot please God, indeed they do not know God. Here he is speaking again of the genuine change brought by the new brith which changes a person. Without that change and the new life it brings, those who profess themselves to be Christian are merely fooling themselves.
John in 1 John goes even further as he says that those who are truly born of God (ie, have been regenerated by the Holy Spirit into faith and new life) will give clear evidence of that fact. They will desire to keep his commandments (1 Jn 2:2-4), walk in a lifestyle that follows after Christ (2:5-6); love his fellow believers (2:9f); does not love this world (2:15f); and does not practice sin as a lifestlye (3:4-10). In fact the whole book of 1 John exists to provide tests for true, as opposed to a false conversion (see 5:13). John more than once says that the one who claims to know Christ, and yet lives in continuing sin is a liar and the truth is not in him. (2:4; 4:20).
Indeed, someone who believes that a person can "accept Jesus" and continue to live in sin yet still go to heaven simply betrays the fact that the do not understand the nature of salvation at all. Jesus said "unless a man is born again he cannot enter the Kingdom of Heaven" (John 3). By that he means, there must be a radical, God-wrought change of the whole heart and mind evidenced by repentance (a turning from sin) and an embrace of a new life in Christ. Anything short of that is not Christian.
The ultimate definition of such gracious conversion is found in Ezekiel 36:25-29 where God says he will take away the heart of stone (that did not respond to God) and replace it with a heart of flesh (that does) so that those who are saved are made clean and begin to walk in all God's ordinances and observe His way. (There are passages in Jeremiah that say the same thing).
I could go on and on since there is so much that needs to be said here. This is so much a part of the "meat" of the Bible's teaching that it really astounds me when people miss it. We live in an age where so many have come to believe that salvation is a merely human decision, rather than understanding that it is a gracious work of God upon the human heart that brings a real and lasting change.
My friend Paul Washer gives a good summary here, let me just pass this short video along.