The issue is discussed on Mormon Matters in two parts; on January 5th, and again on January 20th. President Veazey first introduced it to the general membership in his Counsel to the Church address. The specific legislation index indicates 26 different resolutions to consider.
One of them, G-5 (Policy on Priesthood), is pertinent to this post. One of the clauses states the following:
Whereas, There is no record of Jesus giving any specific instruction about sexual orientation, but Jesus did instruct us to love one another, and in both word and action taught us to embrace marginalized persons;
It's true that Jesus instructed us to love one another, and particularly reach out to marginalized persons, but is there really no record of Jesus speaking out on homosexuality? The fact is, the four synoptic Gospels reveal no counsel or opinion given by Jesus during his earthly ministry. Not once does the word "homosexuality" appear in the four synoptic Gospels. But there are two other facts to consider.
(1). The four synoptic Gospels obviously do not record every single word Jesus spoke during his 33 years of mortality. CNN was not following him around with a camera 24/7.
(2). The ministry of Jesus Christ on this earth was not limited to mortality. Latter-day Saints believe that Jesus Christ was the Jehovah of the Old Testament.
And in the latter case, Jesus Christ, in his role as the pre-mortal Jehovah, did speak out decisively about homosexuality. In fact, the Bible records that Jehovah personally inscribed His opinion about homosexuality on the stone tablets that were destined to become the Law of Moses. Part of that Law of Moses is recorded in the present day book of Leviticus. And two verses in Leviticus spell out Jehovah's opinion about the practice of homosexuality:
Leviticus 18:12 - "Thou shalt not lie with mankind, as with womankind: it is an abomination".
Leviticus 20:13 - "If a man also lie with mankind, as he lieth with a woman, both of them have committed an abomination: they shall surely be put to death; their blood shall be upon them".
Obviously, no Christian denomination promotes Leviticus 20:13 nowadays; the only exception I'm aware of is Pastor Pete Peters of LaPorte Church of Christ, who wrote a pamphlet entitled "Death Penalty for Homosexuals is Prescribed in the Bible". However, conservative Christian denominations continue to use Leviticus 18:22 as part of their scriptural justification to oppose the sanctioning of homosexuality.
But Jesus Christ also speaks through his authorized representatives on earth, who are ordained and set apart for that purpose under Priesthood authority. When ordained missionaries are in the field, they are authorized representatives of the Lord and His Church, and speak officially for both when "on the clock". The Apostle Paul was also one of those missionaries, and he recorded his thoughts about homosexuality in Romans 1:26-27:
26 For this cause God gave them up unto vile affections: for even their women did change the natural use into that which is against nature:
27 And likewise also the men, leaving the natural use of the woman, burned in their lust one toward another; men with men working that which is unseemly, and receiving in themselves that recompence of their error which was meet.
So the next time someone tells you that "Jesus said nothing about homosexuality", you now have the information necessary not only to rebut them, but to expand their understanding about the role of Jesus Christ Himself.