How do I design a quasi tamperproof shower curtain rod mounting point for eldery with Alzheimers?
I think a standard shower rod will work. The brackets screw into the wall, and then the rod rests on some tabs that keep it from moving. Covers slide into place to hide the innards of the bracket. 

This is about as secure as you can get it, without making the rod difficult to remove. You can pull back the bracket covers and remove the rod easily.

Tension rods are notorious for loosening up over time and falling, and would not be a good choice for somebody who likes to grab and pull on them.

I think your concern about the rod needing to be easily removable may be a bit overblown. The curtain can just be pulled aside when you need to clean the shower, unless you have some specialized equipment you need to get in there