Here's how I interpret biblical sexual morality: back when the original Torah was written, fertility was a big issue. Society was primarily agricultural, so families survived by having lots of children so they could eventually help work the farms. This meant that it would make logical sense to prohibit any action that could lead to fewer children (celibacy, homosexual sex, masturbation, contraception, sex outside of marriage, or sexual acts that don't lead to copulation such as ejaculating on the outside of a partner), and if you look at the mitzvot, or Jewish law (which is what our current Christian moral standards for sex are based on), these rules are all mentioned.

However, times have changed now. We're no longer a primarily agrarian society, and our population continues to explode, to the point where it is no longer sustainable. We have approximately 7 billion people, and this doubles every 40 years. Already food is becoming more scarce due to having to feed far more people than we ever thought we would need to, and this is being reflected in food prices worldwide. We will probably hit a point sometime during my lifetime (I'm 28 right now) where our population will hit a critical mass and trigger mass starvations.

Over the centuries, Jewish law has evolved, even though the text has not. Judaism has historically encouraged careful study and interpretation of the texts, which is reflected in the mass of rabbinical texts that have accumulated over the past 5 millenia, beginning with the Talmud, but continuing on to modern times. A similar phenomenon has occurred in Christian thought, though it appears (to my mildly educated eye) to be less prominent.

Keeping this historical context in mind, I believe most of these sexual prohibitions no longer need apply, and indeed, should be discouraged as much as possible. The prohibition against sex outside of marriage still makes (some) sense to me, especially considering the high rate of transmission of STIs, particularly HIV, however by using contraception, that risk can be mitigated. The others don't make a whole lot of sense to me anymore. They don't cause any harm to people in the modern age.

Finally, the mitzvot (there are 613 of them!) are not strictly adhered to uniformly under Christian thought. For example, Christians are not obligated to keep Kosher in their diets, nor are they expected to keep the Sabbath, or to circumcise their male children (this is actually something that was meant to be specific to Jews, as it indicated a man's Covenant with G-d, as one of G-d's chosen people). While Jesus does talk about sexual morality, he never specifies what that involves. And this is the guy who defended prostitutes from judgement by others! Now, I'm not saying that by doing so, Jesus was permitting prostitution, but, I am saying that there is a lot of room for interpretation about what sexual morality entails under Christian thought. Certainly a lot more room than under Jewish law.

One last thing: This is just my personal interpretation. My religious/spiritual beliefs lean toward Judaism, though I am not (yet) Jewish myself. I was raised Christian, and then became part of a Jewish family for years (by way of a very significant other). I suppose that's given me a bit of a unique perspective. By the very nature of my argument leading to the idea that you should seek your own interpretation, I am not saying you need to believe in this interpretation. I only seek to outline one alternative interpretation, though I encourage you to find your own, whatever that may be. Good luck and best wishes on your continuing spiritual journey.