There is a psychological phenomenon that I think is responsible for at least some of the persisting disagreement around philosophical, political, and religious issues. Philosophers refer to it as self deception.
The idea is that when we are attached to a position and are confronted with a criticism of it, we have the ability to push the criticism away rather than thinking about it carefully and honestly. We can do this by simply directing our attention away from the criticism or by brushing it off with some sort of facile criticism that we know on some level isn’t very good. The effect of our action here is to hide the criticism from ourselves because, after it is done, we forget about the criticism and carry on as if it was never presented.
If someone does this frequently, then their view will eventually be completely immune to criticism, because they will have hidden all of the objections to it from themselves. Their view will seem as clear and obvious as the morning sun, even though it is beset by problems on every side. Future criticisms will meet the same fate, since the person in question has established a habit of brushing away criticisms without serious consideration. (I think anyone who has spent any serious time arguing about religion or politics on the internet has met people like this.)
The problem is that to the person who has deceived themselves, their view looks exactly the same as a view that has been established. A view has been established, in general, if there are strong arguments for it and no serious objections to it. This is how a position looks to a person who has deceived themselves, because they have made themselves believe that the arguments in favor of their position are strong and the arguments against their position are weak.
This leads to a practical problem. How can we be sure that we aren’t deceiving ourselves about a political or religious issue that is important to us?
One method that might help is to sit down and explain your position from the beginning. A recent psychological study found that people who held extreme political views often became significantly less confident of their views after they were asked to explain their position step by step, listing every causal connection that their view presupposed. This is consistent with other studies that have found that people become less confident of their understanding of everyday objects like toilets or door handles when they are asked to give a mechanical, step by step description of how the object in question works.
Another method that might help is to write down objections to your position as they occur to you to help prevent you from forgetting them. Darwin allegedly used this method to avoid forgetting objections to the theory of evolution while he was gathering evidence for it.
Neither of these methods is infallible. There are people who can explain their position from the beginning and who write down all of the objections they come across who nevertheless hold absurd and disingenuous views. However, if you are generally honest, being a little more methodical might help you recognize problems with your position that you would otherwise have brushed away.