Quick cross-partisan recommendation: Ask how their policy will work.

Questions are one of the most powerful tools for mind-changing conversations. Asking someone why they believe in something, encouraging them to list the reasons (so you can argue with their reasons) is not typically effective. Instead of asking someone why they believe in a certain policy, especially a complex one, ask them to explain how their policy will work.

The study Political Extremism Is Supported by an Illusion of Understanding
found this to be particularly useful to help moderate extremism. Progressives might want to use this technique around abortion laws, the conservative desire to fight ISIS, or Republican healthcare bills.