Sodom and Gomorrah was God's way of making a very important point. It was relevant to the age, when a minute human population had a vast world to populate and subdue. We don't live in that age.
Some people would answer YES, you can be redeemed and be gay. Those are the moderate and liberal Christians for whom the barn door was left open long ago and the horse ran off.
We (that's me and the Holy spirit) were asked the question: Can someone be redeemed and gay? We're going to use deductive reasoning to pick our way through this and see what we come up with.