Dear New Neighbors,
You didn't say, but I'm assuming you have a laundry room that's outside, like connected to your garage or something. Cuz I know that somebody would have to get IN my fucking house to steal laundry powder from us and I'd have already shot them by that time!
There are a couple of things you could do here. First, get proof of who it is and call the cops. You have a computer, so now all you need is a webcam. They're not that expensive if you don't have one already. I have a webcam plugged into mine that I keep outside the window pointed at my driveway so that with just one click, I can see if someone's here. You could very easily move your computer so that the webcam can look out a window in such a way that it'll see anybody going to your laundry room. There are plenty of freeware programs to record from your webcam (although it may come with such a program anyway).
The second option is just plain mean, but also hilarious. Go buy yourself a shitload of those large bleach tablets that are used to drop into a toilet tank to keep it clean for an extended period of time. Crush them into a fine powder and they'll have roughly the same look and texture of most laundry powders. Put the bleach powder into an old detergent box and leave THAT out in the laundry room instead of the real washing powder. The next time they steal your "detergent" and use it to wash their clothes, they'll get a fucking nasty little surprise. As in, SURPRISE - YOU BLEACHED ALL YOUR CLOTHES!
Both of these *could* be done without involving your parents, but you might be surprised to find that they'd go along with at least one of them. Usually when people give stupid cliche responses like the one your mom gave, it's because they don't actually know WHAT to do about the problem and/or they're afraid of confrontation. The bleach powder option removes the need for any confrontation at all. The webcam option puts them clearly in the wrong and you only have to deal with the cops, not the asshole neighbors. I'd advise going with the 2nd choice, since it's at least 20% cooler than the first choice :)
Of course, there's always the incredibly simple and obvious solution that you should have thought of already: LOCK THE FUCKING DOOR, GENIUS!
Oodles and Oodles of Hatred,