Christians are against homosexuality because God is against it as you have sited in Leviticus, and as we can clearly see in Genesis in regards to Sodom and Gommorah.
Jesus is against it "MK 7:20 He went on: "What comes out of a man is what makes him `unclean.' 21 For from within, out of men's hearts, come evil thoughts, sexual immorality (the Greek word is pornia, which refers to homosexuality), theft, murder, adultery, 22 greed, malice, deceit, lewdness, envy, slander, arrogance and folly. 23 All these evils come from inside and make a man `unclean.' "
And Paul was against it "1CO 6:9 Do you not know that the wicked will not inherit the kingdom of God? Do not be deceived: Neither the sexually immoral nor idolaters nor adulterers nor male prostitutes nor homosexual offenders 10 nor thieves nor the greedy nor drunkards nor slanderers nor swindlers will inherit the kingdom of God. 11 And that is what some of you were. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God."
In regards to slavery, God allowed the Israelites to be slaves for hundreds of years in Egypt. Thus God allowed the Israelites to have slaves, as long as they were not Israelites.
Moreover, God allowed Christians to be slaves in the NT. For Paul told Christian slaves in "EPH 6:5 Slaves, obey your earthly masters with respect and fear, and with sincerity of heart, just as you would obey Christ. 6 Obey them not only to win their favor when their eye is on you, but like slaves of Christ, doing the will of God from your heart. 7 Serve wholeheartedly, as if you were serving the Lord, not men, 8 because you know that the Lord will reward everyone for whatever good he does, whether he is slave or free."
In regards to genecide, God did instruct the Israelites to totally destroy the Cannanites and other people groups, because they worshipped false idols and offered their babies to them as burnt offerings, because they were grossly involved in homosexuality, drunkeness, and so on. But this command was to the Jews, but Christians were told by Jesus who were part of the New Covenant to love their enemies and turn the other cheek.