Would people understand each other better if they knew more about other religions?
The problem is less ignorance than false knowledge. Whoever wants to understand other religions should learn about them from their own scriptures and sources, not only from what their present followers have made of them.
Many people do know something about other religions. They know what the present followers of those religions claim and how they behave. It is precisely this knowledge that often creates the problems. Someone who knows Islam only from what some Muslims say about it today believes they know it, yet knows only a caricature. The same is true of Buddhism, Christianity or any other religion.
Genuine ignorance would almost be better. It would be like a clean slate from which one could search honestly. What matters, though, is where one searches. Whoever wants to understand a religion should go to its scriptures and sources and ask what they themselves teach. Only then does ignorance turn into real knowledge.
Many people do not take this path. The clergy of almost every religion clearly see the follies of others, yet overlook the errors in their own ranks. So the divisions harden, even though each side believes it knows the other well.
The first verse above says that God made people into nations and tribes so that they might come to know one another. The second warns against following that of which one has no real knowledge. So knowing more about other religions does help, as long as that knowledge comes from the right sources and goes together with an honest look at one's own side.