Conversational intolerance is a concept put forward by the author Sam Harris. He suggests that all religious beliefs should be challenged on the basis of evidence, but is not advocating religious persecution.
He suggests that logical investigation and conversation are essential to move forward in every other field of knowledge and that this should now apply to religious beliefs. For example, he argues that radical views in recognised academic subjects are not readily accepted - people expect and even demand logical reasons and robust evidence to support theories. Why should religious views be exempt from such examination?
Just a short answer to a big subject! Read his book - The End Of Faith - for the full explanation.