I've come to realize that there is no "normal" sexuality. Not a single person that has ever lived was "normal" when it comes to sexuality. WE HAVE ALL MISSED THE MARK WHEN IT COME TO OUR SEXUALITY!!! It doesn't matter if we have homosexual feelings or heterosexual feelings (cf. Matt 5:28).
Many I know who struggle with same-sex attractions want to become "normal" and their definition of "normal" is not to be attracted to the same sex but to be attracted to the opposite sex. So for a guy struggling with same-sex attractions, he does not want to be attracted to men but he wants to be attracted to women. But is this any better?
In reality, our attractions and affections (apart from God) should only be guided, if God so chooses, toward our spouse of the opposite sex (Gen 2:24; Matt 19:4-6). So being attracted to womEn (emphasis upon the plurality of woman), is not biblical. Instead, we should be sexually attracted only to our spouse (who in my case would be a woman - my wife). This is what God intended for marriage and sex (Mark 10:6-9; Eph 5:31).
So a redeemed and pure sexuality, would be one in which (if one has been called for marriage) a person is only attracted to his wife or her husband (1 Cor 7:2), and no other person whether male or female (other than God of course). If one is called to singleness (1 Cor 7:7-8), a pure sexuality would be that our affections would only be for God (1 Cor 6:17).