Unsustainable beliefs are one of the hardest thing to overcome. Just countering them with facts is in most cases counterproductive. Instead of persuading, you will inadvertently harden factually wrong beliefs. You will come across as dismissive and aloof. People will not listen.
There is a reason, why people form beliefs. People use first-hand experiences or observations by others they trust.
Bridging the Gap with Empathy
This is where empathy goes a long way. If you acknowledge why someone holds a certain belief and show understanding why this might be a valid belief, you gain a little trust. This is not manipulation, but it forces you to understand their position. You can now talk at the same level and present facts that show limitations of the idea or cannot be explained with the currently held belief. Doing so, you actively allow people to re-evaluate their beliefs. Only hard-nosed conspiracy theorists will shift sideways and change the course of the conversation. Reasonable people, however, will arrive at a new belief, not one that you tried to impose on them, but one emanating from their own re-assessment.