Ignore the Ignorant
Ignorance can lead to confusion, and a feeling of rejection.
So if ignorance is an obstacle to communication then address the real issue and try to not pay attention to the aggressive thick headedness.
If ignorance is a result of innocently not knowing, then gently let the person know there is a better way to consider the issue.
If ignorance is used to shape the conversation--sometimes people try to dumb down because they don't think learning will build them up...If someone is 'acting' dumb, then it is clear they are stuck, not you. KEEP LEARNING.
To get out of 'bad' conversations, try making a compliment or some positive statement.