If you check out the Dollar stores, doesn't matter which chain, you'll notice a lot of that dish detergent, and washing detergent too, is being manufactured in Mexico, not China, so China can fuck off.

But I have to add something for the preppers too: don't throw away your soap scraps. You're probably not doing that anyway if you're prepping but a lot of people do when they get too small to handle. Save them up and simmer them in a pot with water. Always buy extra Borax - 20 Mule Team is fine: you can do laundry and dishes with only that if you must and it's not nearly as harsh on you as most detergents. It'll also soften your water so you can get the most suds out of your soap.

Do you want a 'detergent' or a soap? A detergent, unless it's one of those eco-friendly kind, contains some very dangerous solvents that are hard to rinse off your dishes and you. You shouldn't be needing a solvent to clean your dishes, no matter what kind of crap was left on them.