What does it mean for God to “give people up” to their sin (Rom. 1:24)?

A good way of thinking about this is that when people rebel against God, especially in the way Romans 1 describes it, they view themselves as being freed from the judgment of God: “We are able to do these things and flaunt God’s law, and you Christian people speak about the judgment of God.”

Paul says that the fact that you are doing these things so freely and with a free spirit is actually itself the judgment of God. God has given you over to that sin. In a sense, if that is the kind of freedom you want, then that is what you will have, and you will taste the consequences of it in your own life.

In Romans 1:18–32, there are three occasions where Paul says that God’s response to sinfulness, the way in which His wrath is manifested, is by the way He gives us over to our sinfulness. He gives us over to sin to our hearts’ content, but by sinning to our hearts’ content, we reap the consequences of the seeds that we are sowing to our own destruction.