Caustic soda is sodium hydroxide (NaOH), aka lye.
I wouldn’t add it to a clothes washer, and maybe not to a dishwasher. The reason it prevents film on glass in a dishwasher is because in hot water it attacks the silica and changes it to sodium silicate, which is water soluble. In other words, it actually dissolves a little of the glass each time by reacting with it. (It prevents film from building up on a substrate by removing the top layer of the substrate). The dissolution won’t occur perfectly evenly over time, so if used too aggressively the glass eventually will gain a slightly rough texture and after a long enough time it will have a slightly frosted appearance that is permanent. Sodium hydroxide does this even to the high grade borosilicate glass used in chemistry laboratories.
As for the clothes, sodium hydroxide will also break most natural fibers down over time via alkaline hydrolysis. If you’ve ever had a cotton shirt develop a hole in it over time from bleaching, the weakening of the fibers that leads to the holes isn’t caused by the sodium hypochlorite (which releases chlorine) in the bleach so much as from the sodium hydroxide added to bleach to stabilize the hypochlorite.
So yes, caustic soda is good for keeping glass looking good in the short term, and excellent for getting grease and oil out of clothes, but it damages both in the long term. It matters less with the glass because it removes very, very little each cycle, but it’ll damage natural fabrics pretty reliably in the long term.
Oh, my goodness. Do you know my husband? ;-) He said almost the same thing, but as an engineer he also drew pictures and wrote formulas.