Romans I calls them "reprobate." The Bible teaches they are "given up", "given over", and thus beyond cure, along with those who blaspheme the Holy Spirit (Mark 3:29) and those "who take away from the words of the book of this prophesy" (Rev 22:19), God shall take his part out of the book of life. If one's name is not found in the book of life, ... 
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.