As I go through the list of supposed teaching or positions which Jesus had, this one is such a bizarre statement, I wasn't really sure how to respond. Since the list did not include much in the way of verse references, I am assuming this refers to the woman caught in adultery brought before Jesus in John 8. This is where Jesus utters the now famous words, “Let him who is without sin among you be the first to throw a stone at her” (verse 8), and people usually like to draw attention to His words to the woman, "Neither do I condemn you" (verse 11).
Typically, I have heard or read this used as a don't-be-judgmental argument. Usually it is accompanied by a statement like, "You're not perfect either. Who are you to judge?"
Given the wording of the statement, "anti slut-shaming," I am assuming this implies that Christians are engaged in shaming the more freely sexually active members of society.
Just as a personal observation, this is usually pointed out by people who see no distinction between actual hypocritical judgmental-ism and someone simply voicing a belief or warning a friend/loved-one of what they see as harmful behavior.
I have even had friends who are well aware of the gory details of my past say something like, "Who are you to tell me not to do X? I've seen your misdeeds first-hand." Yes, and I have the scars from it as well, which is why I give the warning.
It is entirely in the realm of possibility for someone, out of a heart of love and caring, not judgmental-ism and hypocrisy, to say, "Hey, what you're doing is unwise, wrong, or even a sin." This absurd idea permeating our culture about being "tolerant" is completely ridiculous. It's not hateful, judgmental, or intolerant to simply tell someone you think they are wrong or their behavior is wrong.
If that skewed idea of tolerance is a person's starting point, then no serious discussion or conversation is possible. We all have to put up with and get along with people who believe and do things differently than we do. Sometimes even on deeply moral issues. It is entirely possible to disagree on these issues without thinking the other person is a vile human being. Thinking otherwise derails any sense of relation or discourse people can have and is utterly useless as a worldview.
Hope I wasn't unclear.
Now, as for the teaching of Jesus on "slut-shaming". Anyone who calls themselves a follower of Christ certainly has no business engaging in hateful or shaming behavior. I am convinced that most of the "judgmental-ism" or shaming behavior that conservative Christians get labelled with is based on the ridiculous idea of "tolerance" mentioned above, not because they are "casting stones".
In the case of the adulteress, amusing the charges weren't bogus, she was actually guilty. At no point is her guilt denied or is her behavior dismissed as being OK. Jesus may not have slapped a scarlet A on her chest, but His lack of condemnation was not acceptance or approval of her actions. In fact, after He says, "Neither do I condemn you," His very next words are "go and sin no more." Jesus is acknowledging that what she was doing was indeed a sinful act and that her life needed to change.
This is not a passage about judging. We all make all sorts of judgments about all kinds of things all the time. You couldn't go through life without making judgments. This is not even a passage about judgmental-ism. There are other passages you can go to about that. As stated above, Christians are called to love and not to condemn based on our own opinions or traditions, but on God's standard.
This passage is about the hypocrisy of the religious elite who were trying to set a trap for the purpose of discrediting Jesus in order to protect their own positions of power. If hypocritical judgmental-ism is indeed the activity a Christian is engaged in, then that would be wrong.
Jesus does not judge or shame the woman. However, He also does not give her a free pass on her sin. He extends her grace and mercy, but those things presuppose wrong-doing or being deserving of judgment in the first place. Then He urges her to go and change her ways.
The important thing here is the attitude of graciousness exhibited by Christ against the backdrop of self-righteous judgmental-ism by the ones bringing the charge. As followers of Christ we are to exhibit the same gracious attitude that Christ had for sinners. If we do not, then we are not following our Lord. But that does not mean we have a permissive attitude regarding sin. We should speak the truth, but do so out of love, not judgment (Ephesians 4:15).