As for homosexuality that is actually specificity mentioned several times in the New Testament. It is one of the very few Levitical laws expressly mentioned as still in force in the New Testament. However, in fairness those same passages also call out those who are adulterous, slanderous, greedy, and drunkards with equal force.
1 Corinthians 6:9-10 (NIV) 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.