My go to solutions are:
!. I see that you tried vinegar and baking soda, but did you try the vinegar with
the baking soda? I have the same problem and use a solution of hot water, vinegar and baking soda... and a fairly hard bristle cleaning brush (not metal bristles). Some people say that vinegar and baking soda is "ineffective" but I have had very good success with it, including cleaning massively dirty pots & pans.
In the past I've used Scrubbing Bubbles (some success, but I hate the fumes); KaBOOM! (some success, but I hate the fumes); CLR® Calcium, Lime, & Rust Remover.
Side note, which you probably know: There is a lot of calcium carbonate and magnesium carbonate in California water. Even if you are using filtered water, if you pour a glass of water with ice, especially if you also have alcohol (gin, tequila, etc) you will probably notice some white cloudy flaky stuff in your drink.
That is the stuff that ends up on your shower door.
The only real "solution" is to stay ahead of it from the beginning... which means wiping off the doors after every shower and cleaning the doors frequently... even once or twice a week... or more... before
the build up starts. It is a true pain in the ass.
2nd Side note: Be careful about mixing chemical cleaners as that will sometimes result in poisonous fumes.
Ammonia + Bleach
Rubbing Alcohol + Bleach
Bleach + Vinegar
Thanks for the information on calcium carbonate. I looked it up online and the pictures seem to mirror my problem, so perhaps that is indeed the culprit. The solution I’m reading is to use a highly acidic cleaner. Most cleaners are alkaline/base (such as products with ammonia and/or bleach), so perhaps that is the problem. Although I have tried vinegar, an acid, but that isn’t as strong.
And, yes, you’ll have an explosion of you combine opposite ends of the pH like that. Vinegar and baking soda actually is such a combination, but they are not as strong on each end, but they do tend to cancel each other out a bit, so this is why it doesn’t work on certain things. I did try it on the shower door.
Haven’t tried CLR, and that’s highly acidic, so maybe I’ll start with that. I’m also reading that toilet bowl cleaner is highly acidic. Maybe I’ll try that as well!
As far as staying ahead, indeed, I have been cleaning all doors regularly on both sides every week. Unfortunately the staining is from the previous owner, who was quite negligent on cleaning a lot in the home. I’ve managed to remedy most of it, but not this.