There may have been a time when the words "judgmental" and "self-righteous" were commonly used in a way that coincided with their dictionary definitions. We are not living in that time anymore. Nowadays, in practice, these words (along with the phrase "holier-than-thou") mean simply: "a moral stance or criticism that makes me feel uncomfortable about myself."
It is now impossible to talk about moral righteousness without being called self-righteous. It is impossible to judge anything without being judgemental. It is impossible to discuss holiness without being holier-than-thou. It is impossible to make a moral argument without being a moralizer.
Our society is filled with people who cannot tolerate moral discussions of any kind, especially if their own life choices are being called into question. Their way to shut it down is to impugn the motives of the person who brought it up. As for the substance of his argument, they have nothing to say. He is a puritanical prig for stating it — no matter how he states it — and that is all that matters.
Anecdotally, I have found that I will be called judgmental and holier-than-thou even if I couch a general moral criticism with specific criticisms of myself. Even if I speak broadly on a subject, and the only person I personally critique is myself, still I am self-righteous. Even if I write entire articles exclusively about my own weaknesses and shortcomings, still it is judgmental because it reeks of religion and morality. The moment people catch the scent of judgment — any judgment, even self-judgment — their defense mechanism kicks in.
I am far from the only one who has experienced this. I cannot tell you how many times a person has confided in me that they wish to be more outspoken about their beliefs, but they are terrified that they will come across as judgmental. They have seen how that label has been hung around the neck of every outspoken Christian in the country, and they do not wish to suffer the same fate. Their hesitation is understandable. But I always tell them the same thing: don't fear the labels. They mean nothing. Speak your mind and let the peanut gallery do what it does.
It's unfortunate that "judgmental" and "self-righteous" have been drained of their meanings by people who instinctively throw the accusations at anyone who breathes a word of moral criticism in their vicinity. Traditionally, the words do speak to something important. Someone who is truly judgmental and self-righteous is someone without humility who does not see his own flaws and weaknesses, but has no trouble locating them in others. He is someone who tends to put himself forward as an example of moral perfection.
It is bad to be that sort of person. But a person is not automatically that sort of person just because he has taken a moral stand of some kind. When he says "this is wrong and that is right," it doesn't necessarily mean that he's claiming to personally always do the right thing and never the wrong. He may not be making any claims at all about himself. If a man proclaims that two plus two equals four, it does not mean that he thinks himself a mathematical genius. It just means that he thinks two plus two equals four. And if we are living in a society where most people deny basic arithmetic, then it becomes necessary for those who do not deny it — even the ones who are very bad at math themselves — to shout about two plus two from the rooftops.
Not everyone who distinguishes between right and wrong is pretending to be a saint. It could be that he is a sinner, and knows he is a sinner, and therefore takes sin very personally and hates it all the more. As long as he acknowledges himself as a sinner, and does not position himself as a paragon of moral perfection, then his moral statement deserves to be addressed and engaged on its merits. He is "judging," yes, but so what? Judging is a good thing, as long as the judgments are correct and made with the right heart.
Contrary to popular belief, the Bible does not actually forbid judging. Indeed, it requires it. In John 7:24, Jesus commands us to judge but offers this qualifier: "Do not judge according to appearance, but judge with right judgment." So, what matters about a man's judgment is whether the judgment is right. A judgment is not automatically wrong just because it is a judgment.
Everyone loves to quote (or paraphrase) that verse where Jesus tells us never to worry about the speck in our brother's eye. The only problem is that Jesus didn't tell us to never worry about the speck in our brother's eye. Here is what He actually said:
"Why do you look at the speck of sawdust in your brother’s eye and pay no attention to the plank in your own eye? How can you say to your brother, ‘Let me take the speck out of your eye,’ when all the time there is a plank in your own eye? You hypocrite, first take the plank out of your own eye, **and then you will see clearly to remove the speck from your brother’s eye**."
Somehow, the last part of that last sentence is often left out. Jesus is telling us that we absolutely ought to help our brother with his speck, but we will not be able to do that if we are blinded by sins we refuse to confront within ourselves. Strive for holiness and then you can help others do the same. That doesn't mean that we must be perfect in order to admonish sin and distinguish between good and evil; it just means that we must hold ourselves to an even higher standard than we hold everyone else. We must be "working out our own salvation with fear and trembling" if we can ever hope to assist our brother in his own walk.
Be humble, in other words. Do not think too highly of yourself. Know that you have sinned and your sins are disgusting and terrible. And then go out and speak the truth, and stand for what is right, and you can be confident that you are doing it righteously, not self-righteously. You are not putting yourself forward as the standard for righteousness. You are looking to God as the standard, and you are urging everyone, including and especially yourself, to strive for that standard.
If people still refuse to even listen to what you are saying, it's because they do not want to see their own imperfections. Ironically, they accuse you of thinking you are perfect, but they are the ones with this delusion. They are the ones who have positioned themselves, not God, as the standard of righteousness. In the end, as it turns out, there is no one more self-righteous than the person who calls everyone else self-righteous.