The following is meant as an explanation for those who are willing to hear it. If you don't like the Bible, don't believe in it or God, then don't bother reading it. Whether you like God or the Bible or not, it's not going to change my beliefs or what is written in the Bible, and chances are I've already heard how you think my God is full of hate, injustice, and He doesn't exist, etc etc or homosexuality is not a choice.
From quote in OP, I would say it's a "ministry" based on fear and a singular message that has nothing to do with the gospel.
The Bible does say that homosexuality is a sin, but it doesn't say to go out and kill homosexuals. The law was given to the nation of Israel, specifically (it's not one of the 10 commandments, by the way), and was intended to serve as a protection for the nation against the corruption of the nation. The law (also forbids divorce, bestiality, etc) was for the authorities in the nation to enforce, not for vigilante justice by hate mongers.
OT law was very strict in terms of punishment for breaking the law, including against rebellious children who refused to heed their parents or the law. The reason it was strict and God prescribed harsh punishments was because it was necessary in order to keep the nation in line and to protect the lineage that would ultimately lead to Christ. Even with the law, you can read how Israel turned to sin again and again, and every time they did they would suffer the consequences of their actions.
The reason Christians don't follow the OT law is because it was never meant for the entire world, and not for all time. Even reading the Torah you see that the law was meant to be in effect until the prophet came who would speak on behalf of God and explain the law (the heart of the law, and not just the prescriptions of it) to them, and bring an understanding of who God was so that humanity could once again dwell with God. Christ, being both man and God, became the reconciler between redeemed humanity and God. Christ came to fulfill the law, and He did so with His coming and ministry on earth.
The heart of the law, as explained by Jesus in the sermon on the mount, is that we are to love God with all our heart, soul, and mind; and we are to love our neighbors as ourselves.
Homosexuality is still wrong because it is against what God designed for man, that sex take place within marriage between a man and a woman who love each other and are married and committed solely to one another. The penalty for homosexuality (death), however, is not what is prescribed in the OT, but whatever the government does or does not impose. In other words, it's not for a Christian to go around enforcing the OT law, but to spread the gospel message of repentance and salvation and to do good works. Note that Jesus didn't go around condemning homosexuals and blasting away perpetrators crimes against the OT law in Israel (the one place the law actually was used for local governance). He didn't go around condemning prostitutes or thieves, either. What He did do was to preach to all those who were willing to hear, and He forgave those who wanted forgiveness. Christ did not come to condemn, but He came to forgive and to build His (spiritual) kingdom on earth. The one group of people that He did have a lot to say against was the group who were convinced they weren't sinners, the hypocrites of the scribes and Pharisees. The repentant tax collectors, prostitutes, etc. He welcomed, and indeed the early church was formed by sinners who wanted to follow Christ and had turned from their former ways.