Is Homophobia a Core Teaching of Christianity?

With the tragic death of Rutgers student Tyler Clementi exemplifying an ugly recent homophobic trend, the central question emerges as to 

whether one can be a good Christian without condemning homosexual behavior (along with the ingestion of shellfish, wearing clothes of a mixed fiber (polyester-cotton blends come to mind), rotating crops, and allowing menstruating women to enter a church or temple (which is apparently offensive to the Lord)).   Most of us find homophobia abhorrent, just as we find Biblically-sanctioned slavery and stoning of adulteresses abhorrent, but there is no evidence that Jesus explicitly condemned the passages in Leviticus used to condemn homosexuality. However, there is one enormous piece of evidence that Jesus was no homophobe: he never once mentioned homosexuality, although he had a lot to say about other specific "transgressions" including adultery.

Thank Zeus that most modern Christians have abandoned these Leviticus injunctions but not because of anything Jesus said.  Rather, times have evolved and so have our mores.  Most importantly, Western governments are now secular, so the church no longer has the power of life and death over citizens as it did as recently as the 1700s.

Although the potential universal appeal of Jesus's message has been seized upon to - among other things - justify its spread to Gentiles, Jesus was a Jew preaching to an all-Jewish audience about how to be a better Jew. The lost sheep he had come to save were Jews who were not properly following the mitzvahs (collected in what Christians have since come to call the Old Testament, although he would have found such a name strange, since of course there was no New Testament that had been written, nor would one be written until decades after he died).
The idea that he had come to replace the law would have been news to him; in Matthew, he told his followers that only if they followed the laws with perfection, every one of them, would they get into the Kingdom of Heaven, which he spent a great deal of time and energy describing:

• 5:17 Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil.    
• 5:18 For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled.   
• 5:19 Whosoever therefore shall break one of these least commandments, and shall teach men so, he shall be called the least in the kingdom of heaven: but whosoever shall do and teach them, the same shall be called great in the kingdom of heaven.
• 5:20 For I say unto you, That except your righteousness shall exceed the righteousness of the scribes and Pharisees, ye shall in no case enter into the kingdom of heaven.  

                    - Matthew 5:17-20, emphasis added

When asked which of the many Jewish laws were most important, he gave various responses, but usually they involved the idea of loving God (Yahweh) with all your heart, not committing adultery, lying, or stealing, and not judging others lest you be judged yourself. The novelty of his message was his expansion on some of the mitzvahs.
He took Rabbi Hillel the Elder's formulation of what has become the Golden Rule to a new level, stating that you should not just tolerate but love your enemy, and if you have a falling out you should promptly make your peace (lest he be arrested and out you), and if he hits you, you should not just not hit him back, but turn the other cheek so he can hit that too!
His message of radical social justice and redistribution of wealth should be familiar to any reader of the Jewish prophets Amos or Isiah The rich are going to hell, Jesus said, unless they give away everything to the poor and follow him.
The only explicitly sexual message he gave was an expanded definition of adultery to include not just actual acts of sex but even sexual fantasies (what Jimmy Carter admitted to in a 1976 Playboy Interview) or remarrying following divorce. These last teachings in particular are said to have left his followers "amazed" but they certainly do not replace the Jewish laws he felt he was enforcing.
He did state that what comes from our bodies (our words and deeds) will condemn us far more than what we put into them (meaning pork or shellfish, for example), but that does not mean he was saying the teachings of Leviticus should be abandoned, only that they could not substitute for being kind to your enemies and treating the poor and outcast with justice.
It is quite clear from his teachings that he envisioned an imminent final judgment approaching that would come before his followers "tasted death" meaning in their lifetimes, which clearly was not the case, but may have explained why he didn't write anything down or if he did, why it was not preserved.
My fear of Christianity is the same as that of Chinese communism: although both have mellowed out quite a bit from their more blood-soaked days, there have been no statutory or formal doctrine amendments that would guarantee that Christians would not attempt to reimpose public executions of adulterers or Chinese would not shut down free markets and go back to the horrors of the Cultural Revolution.
Until and unless Christians come forward and formally renounce those doctrines such as slavery, the murder of accused adulterers or witches, misogyny, and homophobia (which most often involve other Christians), there is always the danger that the darker side of this faith will emerge again.