You cannot just take everything in Leviticus and directly apply it today. That was God's Law for the ancient Israelites, during a time where extreme discipline was required and they were being protected for a very specific purpose: to bring forth the Messiah, Jesus.
In fact, if you follow the Law, we must also "surely" put adulterers to death:
Sodomy is not worse than sleeping with your neighbor's wife and destroying their marriage. Do you know how many people we'd have to kill if we were to literally apply all these rules? We are no longer under the Law, and following it today is not necessarily going to lead to the best outcomes. Although the general principles apply, the most important thing is to bring forth repentance.
The homosexual stuff can easily be tackled by going after the propagandists. And having a zero tolerance approach to public homosexual behavior. Russia has taken a very important step forward by criminalizing gay propaganda to children. These people get kids while they are young, brainwash them, and make them grow up to be a slave of their passions.