Leviticus 11:40 says “If any animal you may eat has died, anyone who carries its carcass…shall wash his clothes.” Just don’t use Downy fabric softener; according to Wired, (but not online at time of this writing) a main ingredient is Dihydrogenated tallow dimethyl ammonium chloride,
The Downy website is much more circumspect and leaves out the dead animal part.
A few of the vegan sites are on the case, and a few manufacturers like Method and Ecover say that they are plant based and tallow free. Seventh Generation makes theirs from canola oil and is even kosher certified. But not everyone gets it; Website Kosher.com sells Downy, which I suspect wouldn’t pass muster in Leviticus.
So if you are vegan and don’t like drinking wine made with isinglass, you sure won’t like washing your undies in animal fat. And who needs the stuff anyways?
