Ask the glass door installer. They probably ran into this issue before and may have a variety of solutions backed by experience.

I've used the little almost invisible bumpers from 3M. I had a shower door that could touch the marble tub surround in my former bath (yes, I did place it on the marble but tiny and discreet no one but me really knew it was there) I use them for cabinet doors, the door leading to outside from my mudroom...any place a handle or knob might come in contact with something. They may slightly yellow after years, easy to replace.

Great for the bottom of a vase, standing photo frame that might scratch, all kinds of uses and I wouldn't be without them.

Are those 2 different showers? Is it a problem with both of them?

If you are concerned about the force of a fast moving door doing damage, then a small bumper offers little protection. A larger bumper would distribute the force more.

@Diana Bier Interiors, LLC: "Are those 2 different showers?"

No, he was standing inside the shower when he took the first and second photos. The door swings in and out.

Yes, it is one shower with the door inside and #2 photo, outside.

Reverse the door swing. Except, that won’t work either. Smaller door with a fixed panel? Nope? It needs to be redesigned. Someone should have seen this way back when it was just a drawing.

Hmmm. I have the exact same door and situation that you have pictured. Our door has some tension on it so it doesn't just swing or move by itself. You have to push it to get it to move. When you stop pushing it stops moving. We have lived in our home for two years and use that shower everyday and the door has never hit the tile or the door next to it. I would have to push it into the wall in order for it to hit. Can your glass guy tighten the hinges? When my shower door installer (my DH) gets home I'll asked him what he did.

I purchased a tube of foam pipe insulation, cut off a 2 inch piece and wrapped it around the handle. Not pretty but it works.

If someone flings the door open with enough force to crack tile, then you've got major other bull in a china shop damage things happening in the house. You cannot pad the world against brutes.