So what happens if you make a 3x white ender chest private with a diamond? How do other players make an ender chest?
The same way. The best way to think about the diamond latch is as a four dye, which is the username of the person that uses the diamond on the latch.
So white-white-white-[PUBLIC] turns into white-white-white-baw179. Anyone can still make a white-white-white-[PUBLIC] chest by default, but only you can make the white-white-white-baw179 chest.
That aside, anyone can USE your chest to access your inventory, so you should protect your chest. You can hide it, or you can remove the diamond by shift-right clicking the latch.