You are missing the issue of repentance. The chaplain is there to help turn their lifestyles around through repentance and faith in the Lord Jesus Christ. You don't have to be in a prison to only find sinners. The difference is, what is your current lifestyle? Have you repented. An ex-homosexual who has repented of his sin would be welcome to lead the choir, I am sure. So it's not exclusive in any way but the repentance and faith requirement. Surely being a Christian leader even in a prison should require that.
You are missing the issue of repentance.
I guess I'm skeptical about the degree and lasting quality of the repentance of any of them - not that some aren't truly repentant, but I'd say it's rare in the situation.