Religions evolve, however. Liberal and False Religions evolve. God Stays the same.
"Thou shalt not lie with mankind, as with womankind: it [is] abomination." (KJV) Leviticus 18:22
"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."(KJV) Leviticus 20:13
"Or do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived; neither fornicators, nor idolaters, nor adulterers, nor effeminate, nor homosexuals, nor thieves, nor the covetous, nor drunkards, nor revilers, nor swindlers, will inherit the kingdom of God." 1 Corinthians 6:9-10 (NASB)
"There shall be no whore of the daughters of Israel, nor a sodomite of the sons of Israel." (KJV) Deuteronomy 23:17
Quoting Leviticus to affirm a narrow band of beliefs is a little misleading. If we take one we must take all of God's word in that book, you cannot selectively recite those verses that agree with you and ignore the others that perhaps would be at odds to general modern societal values. To wit:
"Ye shalt not round the corners of your head, neither shalt thou mar the corner of your beard" - Leviticus 19:27
(Are you cleanshaven?)
"Both thy bondmen and thy bondmaids, which thou shalt have shall be of the heathen that are round about you; of them shall ye, buy bondmen and bondmaids" - Leviticus 25:44 (seems like slavery was ok afterall, so long as they're local non-christians)
I could go on about blind people not being allowed in church, selling ones brother into slavery, wearing different kinds of cloth in the same garment and much more, all of which are mentioned in Leviticus.
Basically it's a completely ridiculous book to even attempt to draw your moral code from.