Just when you try to put God in a box He sneaks out somehow.
We think of God as pure and holy and that would include Jesus but our idea of pure and holy and God's idea of pure and holy may very well be different.
In the linage of Jesus we find four women listed; Tamar, Rahab, Ruth, and Bathsheba. Ruth and Rahab were of a race detested by the Jews. Tamar and Bathsheba were adulteresses. All four were impure, unfit for the nation of Israel and certainly unfit for the linage of the Son of God but they are there which tells us something about what is pure and holy to God verses what is pure and holy to man.
Purity is not necessarily a physical act as much as a spiritual one. God saw the faith in these four women and not just average faith but great faith that enabled them to not only be counted in the linage of Christ but enough to be mentioned in the scriptures. There were many more women that were in the linage of Christ but these four made the list of mention.
God isn't looking for you to be perfect. Your history, your background, your ethnicity, your heritage, are not the things God is looking for, He is interested in your heart. Canaanities were to be killed and the Israelites were to have nothing to do with them, but God saw a woman who had faith.
Our faith moves mountains. It takes us from no favor to favor with God. Our faith opens impossible doors and it trumps any judgment from God that we may deserve.
Don't allow anything to hold you back from believing God wants to bless you today. Take the leap to believe God at his word that "faith" pleases Him. He is just looking for people, no matter who they are to simply trust Him. He will change the world through them as He did with each of these "unholy and impure" women. God makes all things new!