Oh, this murderer wasn't obeying the scripture?
This will be simple, far less than a full explanation, which many better writers with greater wisdom than I, have written.
Let me begin by saying that “All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness: That the man of God may be perfect, thoroughly furnished unto all good works.” So, both the OT and NT is good for man to know, but it serves difference purposes and was written for specific persons and times.
The Levitical Law was setup for Moses and the children of Israel, and not for the New Testament church. For us, we study the Levitical Law portion of the Old Testaments for serveral reasons. One of those reasons is to identify what God calls sin.
This was a theocracy with God’s judgment of sin carried out by men. The law was to be upheld or it brought physical death and/or punishment to the children of Israel.
In the New Testament, all sin is still worthy of death, for it is written, “For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.” There are many sins noted in Scripture, not limited to homosexuality. The works of the flesh will not allow people to inherit the kingdom of God, and sin will cause those to be thrown into the lake of fire.
All sin still deserves death, but God, through Jesus Christ, now through grace is longsuffering with His physical punishment. Death will still come and the second death will follow all those that reject Christ.
Simply because the Old Testament passing physical death upon the sins of people does not mean everyone could freely run around killing all kinds of sinners, nor is that what is done in the New Testament or today.
So sin has not changed, nor the penalty of sin, nor has the holiness of God against sin. The government of the United States of America is not the children of Israel and is not a theocracy. We, as Christians, are to obey the laws of the land, let our officials carry out the judgment of sin (although we do not judge as God does), and are to love and forgive not kill every person that is found to be a sinner. As the Law was a school master to teach us what is sin, Grace allows us mercy to bring us to repentance to God before judgment comes.
There is no contradiction with God, and to have a covenant with the children of Israel and a covenant with the Church does not at all mean He has changed His idea of sin or how it should be punished. You should personally thank God for being born during the age of Grace instead of the age of Law (whereby we all should be grateful), but rest assured the judgment is still death to all which sin and reject the only way to salvation, Jesus Christ, for the forgiveness of such. At the judgment, all that are found unclean (those which have rejected Christ) will be given the second death, cast into the lake of fire.