Owner Julia's Cleaning

Not much. There are non-chlorine bleaches available, but you gotta look hard and pay more. Locally, those products are sold as Seventh Generation.

I know that they use lemon juice as an alternative to bleach/chlorine may not be as effective, I have heard that there is others for pool water, might want to try googling that.

p911

There are hydrogen peroxide bleaches available, some with "Oxi" somewhere in their names, another is Clorox2. Old home methods include alternating baking soda and vinegar. I do my windows and vinyl tile floors with a cup of vinegar to a US gallon of water.

Chlorine used to knock me down cleaning outside showers. I switched to tsp, tri-sodium-phosphate, works just fine. It removes mildew, rinses off easy, a great prep for painting, too. Use gloves. I put it in a squirt sprayer for small jobs, use a garden sprayer for big jobs. It's available at hardware stores and paint stores, no odor,
After you spray it on, you do have to agitate it with a brush to get dirt or mildew off.

Bleach is sodium hypochlorite and is often used for chlorination in the water industry. You should use hydrogen peroxide (H₂O₂) for your client. Once used, it will break down into oxygen and water; it is the nascent oxygen released that does the disinfection. So, unless your client is also allergic to water, which is highly unlikely because that means she will also be allergic to herself, this should solve her problem. A word of warning: H₂O₂ is a far better bleaching agent than bleach itself, so make sure you dilute it well before use.

Out of curiosity, what does a person who's allergic to herself look like ?

As others have posted bleach conatins chlorine.

You might want to investigate other cleaners like trisodium phosphate (available at home depot or lowes- don't breathe dust!) and also Baking soda (sodium bicarbonate.)

milo