Yes, we should shame rampant sexual debauchery
The uninhibited sexual debauchery of modern society has finally made people "woke" to its destructive nature.
No matter what sins we have committed, God can forgive us through the sacrifice of His only begotten Son. The blood of Jesus Christ is sufficient to atone for all sins, no matter how heinous, if we only believe in Him and accept Him as Lord and Savior. See previous articles here and here and here and here.
That, however, should not prevent us from using the Law as a schoolmaster in calling sinners to repentance and faith. This is not because we hate them, but because they are made in the image of God and loved by Him. Shame is a tool to bring them to repentance and faith, or at least to stop destroying themselves. Shaming a particularly egregious example of public sin can also dissuade others from committing the same sin and therefore avoid the consequences of that sin.
Recent high-profile examples of extreme sexual promiscuity have led to a resurgence in the desire to shame such things and even express the kind of physical revulsion and disgust that one would expect to see from coming across a rotting animal carcass. We have been browbeaten into believing that "shaming" sexual debauchery is bad, primarily by feminists and weak men. The uninhibited sexual debauchery of modern society has finally made people, well... Woke!
Proper shame is a wonderful gift from God. It brings us to the end of ourselves and causes us to cry "Abba, Father" while seeking forgiveness. The fear of being shamed also protects us from committing a number of sins, or at least makes us more reluctant to engage in the same behavior that has brought shame upon us before. Shame restrains us just as the fear of a speeding ticket keeps us from exceeding the posted speed limit. Well, by too much, anyway.
Christians should not waste this opportunity that our culture has presented to bring back shame. But we must not do it out of pride, self-righteousness and vindictiveness. We are not better than those we shame, and we are just as deserving of eternal damnation as they are. We should do it with the aim of discouraging self-destructive behavior and calling people to repent and believe. As horrible and tragic as public debauchery has been, God can use that to bring people to Him.