Actually, after using vinegar in the rinse cycle, your clothes may have a hint of vinegar fragrance to them when you first take them out of the washer, but this will be gone by the time you dry them (even if you air dry them).
I have been making my own detergent for 10 years, I only use 1 table spoon in large loads, and as recommended below I only use vinegar in my rinse water. for all my loads.
Using white vinegar in the rince cycle should solve your problem- it helps wash the detergent completely out of the clothing, is a natural fabric softener and helps keep your washing machine from getting clogged by the residue.
No, your clothes won't smell like vinegar after. :)
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