I'd like to open two Keynote presentations at the same time

Keynote can open two different presentations and can be viewed side by side (useful for comparing content of two presentations or moving or copying slides between presentations) but Keynote is unable to Play two presentations at the same time.

Try turning off Mission Control on the Mac:

Go to: Apple Menu > System Preferences > Mission Control

• in the top half of the window, untick all the options and Dashboard to off
• in the lower half of the window remove any keyboard short cuts

click on "Hot Corners", remove any settings in the drop down menus:

Test Keynote again

Reference: Mission Control