Sin is sin. If you believe in God the Father, an infinitely loving, just, merciful, and powerful Creator, denying that you owe everything to Him, refusing to recognize His omnipotence and desire to love and care for you is just wrong. I know, even as a believer it is hard to recognize when I am turning away from God. When I am falling into the trap of thinking I know better, I could do better, I am totally independent and can do just fine on my own. I know. It is hard.
It's hard enough that I have plenty to be personally ashamed of on a daily basis. I recognize that even a "righteous man falls seven times a day." (Prov 24:16) And I am no righteous man, I'm flawed, broken and in need of healing. I've got plenty of my own sin to keep me occupied. If you think I take a dim view of the sin of others, you should be inside my head or sitting in the confessional when I'm reviewing or confessing my own sins. I'm saddened when other hurt their relationship with God, I'm disgusted when I harm my own.
I certainly need to be more concerned with my own relationship with God than with anyone else's, my relationship with God should be the uppermost concern of every second of my life. But as a Christian, as a Catholic, that does compel me to look outside and help others. Most particularly, my wife and children. My marriage vows and my parental vows at Baptism obligated me to look out for the spiritual well-being of my wife and children. I have a professed duty to protect them, to teach them, to lead them to God. At times, that gives me a moral duty to address the people and environments they are in. If I were to a driverless car rolling down the hill, headed directly toward my son, I would be reprehensibly irresponsible if I did not try to protect him, either by taking him out of harms way or by stopping or redirecting the runaway vehicle. Protecting them from moral harm is a greater moral imperative as it has eternal consequences, not temporal.
Recognizing that there is moral truth. That there is absolute good and bad, I also have an obligation to pass that truth on to others. Think of it this way, you see a child working on a math problem, they write 2 + 2 = 5. Now, you know that is wrong. You can just let them keep making the mistake or you can correct them. Which is a nicer thing to do, help them learn or allow them to keep making mistakes? Of course, you can approach helping them in lots of ways. You can be kind and helpful or you can be terse, impatient, rude, or condescending. Being a nice, helpful teacher is certainly to be preferred. You can also have various attitudes about the child when you set out to help them, you can be thinking "He just needs a little help, a little reminder, because he obviously is a smart kid." Or you can be thinking, "What kind of idiot doesn't know 2 + 2 = 4? Is he a moron? Or maybe his parents and teachers are incompetent baboons..." Or many other attitudes. Obviously, the latter is a real bad approach, it is making judgments that you are in no position to make, while the later is simply recognizing there is a right and a wrong answer and the wrong answer has been written down, let's correct the error...
Lastly, there is the reality that most of the things we do have consequences that extend beyond ourselves. Let's take drug-use as an example. Some will try to argue that their use of drugs effects them alone. But, that is dishonest, rationalization. Look at the ripple effects that are the collective result of individual decisions to do illegal drugs... Gang violence, toxic deaths from processing the raw materials, the violent and repressive economies where the raw materials are grown, the "wars" fought for the land and manpower to produce those materials. Then the lives that are harmed when a person becomes, inevitably addicted to those illegal drugs, parents losing the life savings, homes, property trying to help their child, children losing or never having parents, violence, theft, and other crimes committed by addicts trying to get their next fix. Maybe an individual can honestly and truthfully do drugs, not become addicted and not adversely impact the life of anyone around them. But, certainly that is a rare, rare exception.
When it comes to sin, it is inevitable, our bad choices will hurt others. If you don't believe it, you just haven't taken an hard, honest, objective look at the choice and the real consequences.
So, whether it is to directly protect my family. Or it is to protect society I have some obligation to speak the truth about sin. I have a greater, more profound obligation to deal with my own problems. But, sometimes, dealing with my own problems necessitates or benefits from helping others too.
Think of it this way: Sin is falling into a deep well. But, we all fall into the same well. Definitely, I need to think about how am I going to get out. The only person I really exert any control over is myself. But, if I simply focus on myself and ignore everyone around me, I'm probably never getting out of that well. However, if I recognize my predicament, I retain that profound sense of personal accountability and responsibility, but also turn to those around me and say, "Hey, if we help one another we can get out of this pit." I've got a real chance at escaping.