If they haven’t repented of gross sexual sin (meaning, acknowledged it as sin, and made a great effort to stop the behavior), then they are not true Christians
So you say they are saved by works. But that is NOT what the Bible says. The Gospel of the Grace of Christ in Scripture declares that we are saved by grace WITHOUT OUR works, because of the perfect work of Christ upon whom God exhausted ALL his wrath, condemnation, and punishment for the sins of the whole world (1 John 2:2). IT IS FINISHED!!!