Today when I set up my Keynote presentation, the "presenter view" appeared on the audience screen and the audience view appeared on my MacBookPro. The MacBook is a brand new computer and the Keynote is ver. 6.5.2 (2119) I have used this same computer, Keynote and projector for the past 4 months and never had this problem. I tried disconnecting the computer from the projector and restarting Keynote. No difference. I disconnected the computer from the projector and restarted the computer with the projector connected. No difference. I looked in preferences but did not find anything helpful in the display settings. I'm obviously missing something. Has anyone had a similar experience?
When that occurs, you can move your cursor to the screen with the presenter view (in this case the one that everyone could see); some options will appear, including the ability to swap the displays. This will cause your computer's display to become the presenter display and for the "public" display to just show the slide content.