Ivory soap will not have a detrimental affect on compost. It does not kill bacteria. Why are you asking the question? Antibacterial soap would have a detrimental affect.

Lorna

All soaps kill bacteria, all soaps are really anti bacterial. The USDA's Food and Drug Administration came out 3 or 4 years ago now and said that the antibacterial/antimicrobial soaps are no more effective at killing bacteria then any other soap, and that the manufacturers should stop making and selling them.
How any given soap will affect your compost depends on the volume of soap you put in that mix, as well as how active the bacteria in your compost are. You can put small quantities of soaps and soap mixtures into your compost where they will be digested, eventually.

I concur with Kimmsr and the USDA that the use of the terms antibacterial/antimicrobial are misleading if not in fact flat out wrong.

My undergraduate major was medical microbiology, many decades ago, and -- forgive me, I am too old to enter a fray about anything where my knowledge is shaky and dated.

I would not hesitate to add soapy water to my compost.

Just out of curiosity, why is the detergent getting to the compost? Ivory dish 'soap' is pretty much just like all of the other dish detergents on the market. (Their bar soap is a different story.)

I beg to differ, I've done quite a lot of reading on soaps. Simple soap is meant to create a slippery surface to slide germs off via proper lathering and rinsing. Do a search on hand washing, you will probably be surprised. Antibacterial dish soap kills plants, simple dish soap does not. Ivory is a simple dish soap.

Medical people used green soap in my day, which is highly antibacterial. I used to be a dental assitant. We were required to scrub hands and nails with green soap as soon as we entered the clinic. Don't know whether they are still using green soap, or now use something allegedly new and improved.
Lorna

If you use Grey water, or if you empty a tub of soapy water someplace other than the drain that leads to the waste system, you would be placing soapy water on where you dumped it. That could be the garden, the compost pile, maybe the grass. Seldom, after washing the car, do I take the soapy water in the bucket into the house to put down the sink drain it will go into the compost or on the garden someplace.
Lorna, you could find what the Food and Drug Administration had to say about those antibacterial/antimicrobial soaps by searching their web site. Simple logic does not necessarily follow the sale and use of these products. The Michigan Department of Commerce requires all day care and pre school places to have the antibacterial/antimicrobial soaps on site, but are is telling these places to not have children wash with them because that "might" limit the childs exposure to "germs" and limit the development of that childs immune system, but they do not tell people that the use of those products allows disease pathogens to develop immunities to antibiotics/antimicrobials.

lorna: I work in outpatient surgery centers. Now there are several antibacterial soaps available for surgeons and scrub nurses to use. One surgeon can't use them because of skin problems- he uses Oilatum soap which is gentler I guess. There is no policy on what kind of soap they use, only a specific method of scrubbing with a brush for, I believe, 5 minutes before the first case of the day. For subsequent surgeries, most use chemical antibacterial gels.

Here's a link about handwashing technique in general.

Karen

Here is a link that might be useful: Handwashing

I have been against the general use of the antibacterial soaps since they were first marketed to the public. There are a couple of rants to that effect on one of my old Web pages. I am well aware that the bacteria ecosystem is being badly affected by antibacterial products, creating super strains. Of course, the overuse of antibiotics is also a prime contributing factor regarding the advent of super strains.

Simple soap used in the garden to kill insect pests does so because it coats their bodies causing insects to suffocate. Master gardener Jerry Baker claims that the use of simple soap in the garden has other good affects, such as washing the residue of airborne pollutants off grass and leaves enabling them to breathe properly.

Lorna

Lorna, be aware that Jerry Baker is a self appointed "Master Gardener".