Who says homosexuals are "given up on"? I see where they are given over to their lusts but some of these have been saved. I don't understand the given up part.
Not sure how you are seeing a difference here. If God has given up on them or given them over to their lusts means the same thing. Where Hamel gets it wrong is that he narrows it down to just homosexuality. That is not the reading or the context of that passage. If he will look closely the reason for giving them over to their lusts (ie homsexuality, drunkeness etc) is because the rejected God. This is made clear in v.21 look here:
Romans 1:21
Because that, when they knew God, they glorified him not as God, neither were thankful; but became vain in their imaginations, and their foolish heart was darkened.
In vs. 32 it says:
Rom 1:32
Who knowing the judgment of God, that they which commit such things are worthy of death, not only do the same, but have pleasure in them that do them.
So they knew God, they understood that there is a God, they understood their need for God and they understood His judgment and rejected Him anyway. The homosexuality and drunkeness etc. just grew all the more because God reached a point where He turned them over to themselves. Verse 26 says that God gave them up.