Why does powder soap leave white stains on my clothes?

Chances are you got hard water, which does not mean you been tryin to wash your clothes in ice. There's a few things that happen when the water is hard. But first soap as opposed to detergent is more liable to leave residue, but I assume you actually mean powdered detergent. There's a kind of self escalating problem with hard water and detergent. First the detergent just doesn't dissolve as easily as it would in softer water. The minerals in the hard water are occupying some of the space that the detergent should be, some of the minerals can actually react with the detergent more directly and form a non dissolvable compound that is difficult to rinse off.. Because of that nondisolving the directions on the box may actually tell you to use more detergent in hard water and while that may help the actual cleaning action it just leaves more detergent to stay on your clothes as well as making more scum. Using hotter water can help dissolve more detergent but that is not always possible.
The real answer is to use soft water. Either by using a machine that replaces some of the minerals with others that don't interfere and react the same way, or by adding specific products ( Calgon, RainSoft, etc) to the washer. You can buy them in the same aisle you get the detergent.
Another solution to help the solution ( Hah, thatt's a good 'un, well not really) anyway a solution is not to use more detergent but to use more water, the detergent has more water to go into sollution in. In fact that could actually be your problem, you got too many clothes in there for the amount of water, the detergent is just not rinsing out after the wash cycle. So don't overload the washer. If you are washing smaller loads and have a washer that let's you set water levels and does more than one rinse, overfill the washer by about half as much again as you would ordinarily use but don't increase the detergent amount.. If you stay close and can catch it when the first rinse happens use even more water than that, then you might get by with resetting it back down to a 'normal' level on the second rinse.
If you cant or don't want to use so much water then you need to use LESS detergent per wash and maybe have to actually wash things twice so whats the difference?.
Avoid the use of liquid fabric softeners that you add to the rinse water, they can react with any detergent left in the clothes, especially in hard water. If ya gotta use them predisolve it in about 4 times as much water before pouring it in. That means you can't use the automatic softener feature if your washer has one.
A cup or 1/2 of white vinegar added to a load of wash might help, or you can add the same amount to a first rinse. Usually even if you only add it to a final rinse there is not enough to leave any odor. In fact the vinegar will cut down on any musty odors in laundry as well as cut down on lint. rinse
Other things to check, if using hot water make sure the water IS hot enough, make sure the tub drains completly between cycles, check for mineral deposits in the tub itself. A final solution would be to move to the tropics and wear only white clothes.

It is a truism that all cleaning products recommend that you use an amount that is about twice what you really need. This is true whether it is shampoo, laundry detergent, Pinesol for your floor, liquid or powder. I heard this many years ago and always found it to be true. Never use the recommended amount unless what you are trying to clean is particularly dirty or greasy. Not only will you save money, you will be sending less product down the drain into the sewers, on into the sewage treatment plant and out into the rivers and the whole water cycle thing.

To get back to your question, if you aren't using hard water, as hypothesized by ntmrjohn, you may just be a. using too much soap for it to dissolve properly; b. overloading your machine so that the rinsing is not effective; or c. setting the water level too low for the quantity of clothing that you are putting in the machine.

Also, as my comment to the aforementioned notmrjohn mentioned, you can always try switching to a liquid detergent; not only does it not have all the powdery fillers that end up as residue on your clothes, their purpose is to 'grind' your clothes clean thereby wearing them out faster.

Let me know if this helps.