There are three times where Romans says "God gave them up or God gave them over. The sins of homosexuality among the other sins occur after God gave them up. Any time scripture repeats something 3 times it is a clue to pay careful attention.
Romans 1: 23 exchanged the glory of the immortal God for images made to look like a mortal human being and birds and animals and reptiles.
Romans 1:24 THEREFORE God gave them over to the sinful desires of their hearts.
Romans 1:25 They exchanged the truth about God for a lie, and worshiped and served created things rather than the Creator—who is forever praised. Amen.
Romans 1:26 Because of this, God gave them over to shameful lusts.
Romans 1:29 Furthermore, just as they did not think it worthwhile to retain the knowledge of God, so God gave them over to a depraved mind, so that they do what ought not to be done.
In each case God gave them up because they rejected God even though they had adequate knowlege to have chosen differently. So that they are without excuse. What Romans is saying is that God is not rejecting them because of their sinfulness (homosexuality etc.) It is telling us that the depravity is a symptom of the uselessness of their thinking directly caused by the fact that God gave them up because they rejected Him. Homosexuality trans etc. is a mental illness that occurs because of a wholesale rejection of the creator.
Sometimes we get the chain of cause and effect backwards and think that God is angry with homosexuals because of their behavior when a careful examination of the owners manual shows that they are so depraved because they have rejected the ground of their being.
correct!
The declination into evil begins vv18-21.
Every consequence after that is a result of 1:18-21
Neither glorifying God, nor being thankful to Him.
The root cause
...that is all