Our thinking is influenced by everything that happens to us, everything we read, and every interaction. As we assemble these influences, facts and opinions we form a picture of our personal world and other people's worlds. But not every input to our consciousness has the same weight; otherwise we could never come to a stable understanding of anything. Instead we construct inside our heads a framework that represents our personal reality and we appeal to this whenever we are exposed to a new influence; our personal reality weights each new influence so that this reality doesn't oscillate widely. Most often the new influence is given a negligible weight; only rarely is the new influence given a weight so high that it transforms our reality.
These personal realities are often called world-views. If we think about our world-view we are thinking about the totality of our life's experience and the various weights that we give to each aspect of it. These experiences and the weight we accord them comprise our beliefs. Our world view is a large set of separate beliefs that we have tried to organize into a consistent whole. Some of the beliefs of our world-view will be shared by many other people, especially those parts that represent facts about the physical world; but some of our beliefs will be at great odds with other people's beliefs.
Indeed it frequently happens that we hold conflicting beliefs within our world-view. Much of the time we are unconscious of such a conflict and there is not much to be done about this unless we critically and constantly examine our beliefs. This perhaps is behind Socrates' dictum that the unexamined life is not worth living. When we come across such a conflict surely the noblest act is to honestly readjust our beliefs so that they come back into harmony. But sometimes, lazily, we put the conflict aside with a mental shrug. The conflict may have come to our notice because of some fact, newly learnt, and we have dealt with it by assigning it a very low weight in our framework of concepts; or it may have arisen from the Socratic discipline of systematically examining our beliefs for inconsistencies. Probably every single person's world view has such suppressed inconsistencies. If we have made a determined attempt at suppression we can feel a sense of unease when we confront (or are made to confront) a conflict, a sensation that is called cognitive dissonance.
There are several ways to deal with our personal cognitive dissonances. We can adjust our beliefs which can be embarrassing and painful. We can forget them entirely, hoping that we shan't ever have to confront them. Or we can create excuses of various complexity. This is a very common thing to do. When we notice other people doing this (and it may be very obvious when they do) we often deplore their inconsistency. But we are much blinder and more forgiving when we do it ourselves; we forge for ourselves a complex personal narrative which justifies our mental gymnastics.
If we are subject to cognitive dissonance we are always in danger of being wrong-footed, possibly acutely embarrassed, when our mental inconsistency surfaces among our friends and acquaintances. Therefore most people prefer their world-views to be as internally consistent as possible. Yet to form a consistent world-view from scratch (even over years) is very difficult. Therefore most of us bring some pre-existing package of consistent ideas into our consciousness that partly (some very largely) forms the core of our world-view. Some of the philosophic traditions, such as Stoicism or Epicureanism, served the Greek and Romans very well in this regard. Religions and other ethical systems are also used. For many people, a commitment to naturalism is important. These partial world-view packages generally can't give us our entire world-view of course. For example, the Christian package generally won't inform us accurately about whether we can trust our senses as a way of understanding how the physical world fits together. Nor will the naturalistic package necessarily inform us about good ways to conduct our personal relations. But they are definitely a start, and they enable us to piggy-back on the wisdom of our forebears.
Obviously some world-views are more successful than others. If your world-view is constantly producing cognitive dissonance, or hampering your effort to be happy and productive because it consistently leads you to poor decisions, you are worse off than someone whose world-view serves them well in guiding their thoughts and their interactions with their fellow human beings. What types of world-view are successful? That of course is a question too large even to scratch the surface of in this brief post but, nevertheless, I do have some opinions that I cannot refrain from offering!
I think you are going to be in severe trouble if your beliefs are at odds with what humankind has discovered about the natural world. If you are a flat-earther, or a denier of evolution, or you are very superstitious your life is not going to be able to take best advantage of centuries of scientific endeavour. In other words I do recommend the naturalistic package.
I also think it is very worthwhile to think about incorporating some sort of ethical package: virtue ethics, consequential ethics, utilitarianism, Islam or some other religion. Be aware though that these packages don't always lead to sensible conclusions; they only serve as a useful guide in commonplace situations. Indeed in almost every ethical package there is the possibility of coming to contradictions (for example, fundamental Christianity is, in my opinion, necessarily so rife with contradictions that it is worthless).
I think it is useful to have some way of resolving your cognitive dissonances when you notice them - and burying them or ignoring them entirely is obviously not what I suggest. If the dissonance is a disagreement between facts or what you thought were facts I would advise doing some research into what is actually known. That might not solve the dissonance because there may conflicting opinions on what reality is; then you will often have much more work to do. I think it is worth cultivating a depressed ego so that you can relinquish opinions even if you have previously espoused them in public. Obviously this advice won't suit everyone because, for some people (politicians, for example), it is more important to have an unchanging message than to be internally consistent.
Finally I think it is important to be self-reflective, constantly examining your beliefs, and constantly rooting out inconsistencies. This is a habit that needs to be cultivated. Personally I know that I still have a long way to go but the journey is a fascinating one.