I understand that this isn't really a gluten issue but those with sensitivities may prefer to make their laundry soap to avoid additives. This recipe from Just in Case by Barbara Salsbury (1975) is simple but time consuming (it takes a couple of weeks to make soap so it's not something you make and have the next time you wash laundry). However once you get into routine, you will always have laundry soap.
You will need to start off with 5 pounds of grease. In the past we have purchased fat from a butcher and fried or boiled it. This is a quick and cheap way to get a large quanity of grease, however it is best done outside since it will make your kitchen greasy. When you use homemade grease - you have to melt it in water, let it cool so you can remove the particles that come with grease. When the fat is cool, take it out of the water and flip it over. Scrape off particles. I often do this twice to make sure I got everything - using clean water each time. You can purchase lard, shortening, coconut oil or any oils to make soap. With laundry soap hardness does not matter as much as it does with bar soap but remember the softer the oil, the softer the soap. Also remember some oils can get very expensive. If your cooking oil goes stale, you can use it here - the oils do not have to be in good edible condition (my grandmother once made soap with rotten fat, the soap was ugly but it worked very well).
In addition to 5 pounds of grease/oils you need:
1/2 cup ammonia
1/2 cup powdered borax
1 cup kerosene (lamp oil)
16 oz lye (lye is becoming more and more difficult to get in stores - check your local hardware store first, make sure the product is 100% lye. I was able to special order a case of Red Devil before they stopped manufacturing it. If you can't get it at a hardware store there are many online soap making sites that sell lye).
Dissolve lye in one quart of water in a non-reactive pan. I use enameled metal pans that I save just for soap making. Use only wooden spoons and save them for soapmaking. Lye is toxic so you want to seperate all the things you use for soapmaking from cooking items. Dissolve Borax in 1 cup of water and add to lye. Melt grease (don't heat past melting point - in fact I get it almost melted and remove from heat and stir until all melted). Add ammonia and kerosene to grease. Slowly and carefully pour grease into lye (do not reverse this). Stir until thickened. Now the original recipe has you pour the soap into a mold and then grating it two weeks later when it has hardened. We discovered that if you keep it in the pan and over stir it - the soap turns into a powder. The first night stir it as long as you can after it has thickened and then stir it at least once a day for several minutes. You want to stir out any lumps and keep it loose. After two weeks you can use it as laundry soap. If you try soapmaking and have a failed batch you can grate it for laundry soap as well.