Q2. (Jude 4) In what way does sexual sin deny Christ? If Paul is right in 1 Corinthians 6:9-11, that persistent sexual sin is incompatible with salvation, why have we Christians become so complacent about it in our culture?
Two parts to this question and the first as I see it is if we indulge in sexual sin we are feeding the flesh which is under a death sentence from God and also we are quenching the (Holy) Spirit. The flesh and the Spirit are at war and the one we feed will prevail. Surely we are supposed to deny the flesh and avoid the 'works of the flesh' otherwise we cannot inherit the Kingdom of God (Gal 5:19 MKJV Now the works of the flesh are clearly revealed, which are: adultery, fornication, uncleanness, lustfulness, 20 idolatry, sorcery, hatreds, fightings, jealousies, angers, rivalries, divisions, heresies, 21 envyings, murders, drunkennesses, revelings, and things like these; of which I tell you before, as I also said before, that they who do such things shall not inherit the kingdom of God.
Jesus died so we could be set free from the lusts of the flesh and we are also to reckon ourselves to be dead to this world - and all its lusts. Also all of the sins people get involved in don't involve the body like fornication and we are to avoid it.
Part 2 of the question - about why we are so complacent to it... this is because of the lack of the fear of the Lord in the church, and the effect of the entertainment media. We're saturated with it from TV, movies books etc where people have affairs with never any hint of remorse or consequences so after a while in our eyes it drops from being sin, to being a "mistake" - like dropping an egg on the floor, to eventually being excusable and even desirable.
Cheers
Petero