I have some knowledge of this, but not enough to be an expert. Soaps, and soapy water, are toxic to insects, and also microbes, including bacteria living in the soil. Therefore, if enough soap is applied to a compost pile, it will halt the decomposition due to bacterial action, and stop the pile from heating up. However, people do water their lawns and gardens with "greywater," washwater that still has some soap or detergent in the mix. Generally, this practice does not kill the lawn. So it really depends on how much soap, and how often you apply. Given time, I suspect that both a compost pile and soil microbes will recover from being exposed to soapy water.

Soaps might, or might not, cause problems with compost and soils because they can harm the soil microbes. However, many soaps are also digested by some soil microbes. It depends on the dilution.
Insecticidal Soaps, a mixture of about 2 percent soap to water, are used to control some insects, but do no harm to others, but only while they are wet. Once dry soaps do not have any activity to harm insect or soil microbes.

On the contrary Kimm, soap allowed to dry on any insect will cause much harm, probably an early death.
When using "soap" (as opposed to detergent) spray on houseplants to control pests, it is then given a wait time,usually 10 minutes, then a thorough rinse must be given otherwise it can harm plant tissue.

Try it on yourself. Work up a lather on your skin and let it dry.
Soap is an astringent, it dries out the skin--same goes for insects, it clogs their breathing systems.

As far as whether soap can harm a compost pile....well, is there any good reason to put it there.
Depending on the strength, surely soap would do harm to the microbial action there. If one wishes to take a chance on the result from such spraying, then go to it.
Its much easier just to put a cover over the pile and spray as you like.

Soaps, real soaps and not detergents, do not "clog" the insects breathing system and more than they would yours as you lather up in hte shower. The fatty acids in Insecticidal Soaps disolve some insects exoskeleton and once dry have no adverse affect on insects, plants yes, but not insects. Anti bacterial, anti microbial "soaps: (these are actually detergents) can have an adverse affect on soil bacteria or the bacteria in a compost pile, but the major concern with these is that disease pathogens, exposed to small amounts of the antis in them, will develop immunities to those anti bacterials which presents big problems to us.
When you wash you hands with soap and water you put on yuour hands much more soap then you would put on any plant, so that allusion is not a good one.

I assume from the original question you mean incidental splashing, misting, or spillage from the activity of washing the fence, rather than pouring bulk quantities of soapy water on compost or soil...

It would certainly depend on the soap. If it is a natural biodegradable soap it will break down in the long term, even provide some nutrients for microbes in the form of free fatty acids. If not too concentrated it shouldn't cause major disruption in the short term either.

On the other hand, I wouldn't use any commercial cleaner that has toxic salts or synthetic solvents. Also take into consideration what you might be washing off the fence, such as paint.

Yes, it's incidental splashing and what soaks into the ground. Thanks, will be careful and look for the least hazardous cleansers.
Thanks everyone!

Usually soap/detergents are made of potassium and/or sodium with some other things, and maybe sodium is what you should really worry about. And maybe they can be used to act as quick potassium fix? Any ideas on this?

Most all of the "soaps" you buy today are really synthetic detergents. They should, today, be phosphate free, but just what is in them is difficult to determine because the manufacturers are not required to tell you.
Be aware that some of the powdered laundry detergents can cause burns if some is left on the skin long enough.

You might try a bit of the soap solution on a plant to settle the good/bad question. I think I would be tempted to use plastic/drop cloth to cover nearby plants/compost pile. A bit of extra work, but saves a lot of worry. If the solution can wash off dirt/paint, sounds like it might be too strong for plants.

I have whitefly in my compost piles that have been composting over the winter in different airated plastic boxes - how do I get rid of them without ruining the compost, which is reasy to use ?

Wish I knew the answer but I'm not real sure. How about turning and mixing them all together and leaving it in the hot sun, and turning again every day or two. It might kill and/or drive them away.

You might want to post this as a new thread, since the question is not really related to composting detergents.