The Bible however does say as you point out so well (excellent graphic) that there will be those who continue to live and promote gross sin such as homosexuality.
Some people on FR need to understand that the acceptance of or indifference toward homosexuality is horribly destructive and is symptomatic of a perverse culture that is on its last legs of rebellion against God.
The Bible does not contradict itself. If it does, it is not the Word of God. I know that the modern translations render "malakoi" (masc. plural) and "arsenokoitai" (fem. plural) as "male prostitutes" and "sodomites", but there are no other usages within the NT to comfirm. It seems unlikely that such translations are correct in light of Romans 1:28 which makes it clear that such are "reprobate" and "given over", "given up" by God. Clearly "malakoi" and "arsenokoitai" whatever they mean can be saved. The KJV translates "malakoi" as "effeminate" ("marked by weakness and excessive refinement--ladies' men?) and "arsenokoitai" as "abusers of themselves with mankind" (women who hop from bed to bed?). If Paul had meant active/passive homosexuals, male or female, he could have used other Greek terms and phrases.
I didn't want to believe it at first, but true sodomites who burn for members of the same sex have reached a stage of their depravity where God ceases to strive with them and gives them up. (see Romans 1:18-32). They are reprobate (see "reprobate silver", rejected--Jeremiah 6:30 "Reprobate silver shall men call them, because the Lord and rejected them.). We see here that "reprobate" means "rejected".
What do you mean by "repent"? What saves is "belief on/in the Lord Jesus Christ", not "repenting [from sin]"--a work. See Jonah 3:10--"And God saw their works, that they turned from their evil way; and God repented from the evil, that he had said that he would do unto them; and he did it not." Now, if they change their minds (repent), change from unbelief to belief ("that God hath made that same Jesus, whom ye have crucified, both Lord and Christ." Acts 2:36-38), then they shall be saved. "He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God." (John 3:18)
It is a terrifying picture which emphasizes that the lost have an unimaginable eternity in store for them.