Are you able to grasp the door from the back at the bottom of the mirror panel? It seems very odd that there was no provision in the design to keep you from touching the mirror.

I have a mirrored medicine cabinet, you have to push on it for it to pop open. Fingerprints are always an issue. I wondered if you found a solution for yours? Seems like there should be something that I could attach to touch instead of the mirror itself but I can not think of what to call it! Not a handle, but something that is hardly noticeable.

Try glass door pulls.

I have the same issue and am thinking about three options: a thin strip of matte film across the bottom, acrylic stick on knobs or small cabinet finger pulls (might require padding out the door on the inside since they are made for a thicker material.)