I'm gonna disagree with everyone here who is saying just "don't". Sometimes we argue with idiots not to convince the idiot, but to convince the people listening to the argument.

I generally take the view, your job is to say this is what I believe and its supported by these facts. Or I disagree with you, and here's my thinking. Let people see the inner gears of your thoughts and it will persuade neutral parties. If your goal is to persuade someone who wont be persuaded, humbleness and a lack of hostility are often the best course.

I actually think Joe Rogan who has the most succesful podcast in the US (I am otherwise a fan of him generally), does this better than anyone. He has found a way to ask questions of people he may not agree with that allows them to explain how they approach the topic...I personally think he is too laissez-faire on many things but I think that's why he is so successful.