The way I was raised, certain people were simply wrong. If they didn't share the same enthusiasm for science, they were incorrect. If they believed in a benevolent (or even malevolent) Christian god, they were wrong. There was very little gray in many of the positions that were espoused to me. One of the great aspects of humanity is that we are given the opportunity to raise our children with our values and beliefs. But, of course, there are responsibilities there too.
It almost seems absurd to say this, but I don't think I was always responsibly educated. Absurd, because that's a high bar and I'm not sure anyone can ever claim to have been educated under the perfect paradigm. But to the extent that it took me many years to understand what it means to pursue a free and responsible search for truth and meaning, I think there could have been more openess to what I was exposed to. The Christian Bible is an amazing book. The Bhagavad Gita is absolutely beautiful. Darwin had his doubts about the extent to which evolution allows us to understand life. Newton was downright crazy half the time.
The source of responsibility in our lives is humbleness. When we say we are responsible for our children, that does not mean if we fail to teach them the right things we have failed. It means if we fail to listen to them, and discern what they need based on what we understand about them and what they tell us, we have failed them. There is no test for responsible parenthood, just as there is no test of responsible searching for meaning in our lives. When we have the freedom to search for truth and meaning, we must use discernment and listening as our foundation for responsibility. Listen first, think second, act last.