Chemistry - Does bleach (without rinsing) leave residues and can vinegar, baking soda neutralize them?
Solution 1:
After a thorough wash, rinse and dry cycle, little or no bleach should be left in the fabric, but there is possible concern about the effect of chlorine bleach on organic compounds. However, if disinfection is needed, then the infinitesimally small risk of VOC* is outweighed by the elimination of microorganisms.
If any remaining smell of chlorine bothers you, an extra water rinse should be helpful. @Brian suggests a reducing agent, and $\ce{Na2S2O3}$, sodium thiosulfate, is inexpensive and is commonly used to remove residual chlorine for aquaria. However, leaving garments to air-dry or airing them for a day would be as effective.
(*) "Volatile organic compounds"
Solution 2:
Question 1
No. Bleach requires something to react with in order for it to be consumed. There will still be bleach residues on the material.
Question 2
I think this question is actually based on a misperception, likely due to the multiple senses of the English word 'neutralize':
neutralize, verb
: to stop (someone or something) from being effective or harmful
: to cause (a chemical) to be neither an acid nor a base
While you are completely correct that adding acid to sodium hypochlorite would neutralize it in the second sense, you would in fact be doing the opposite of neutralizing it in the first sense. Your 'other source' is correct -- adding any acid to sodium hypochlorite will shift the equilibrium toward hypochlorous acid ($\ce{HOCl}$), which in turn equilibrates with molecular chlorine ($\ce{Cl_2}$), which is a nasty character you don't want to mess with$\dagger$.
What you need in order to neutralize it in the first sense, since bleach is an oxidizer, is a reducing agent. My recommendation would be to, say, crush up a few dye-free vitamin C (ascorbic acid) tablets, dissolve in a bucket of water, and soak the article to be treated for half an hour or so. Note that I've not ever actually tried this, so I have no idea if it will work. It might also work to pour such a vitamin C solution into the 'liquid fabric softener' fill area of a washing machine, if it has one.
EDIT: I just came across this Chem.SE question from two years ago, which confirms that ascorbic acid is suitable for scrubbing of chlorine/hypochlorite.
$\dagger$ Note: Technically, since $\ce{Cl2}$ is volatile, soaking the material in an acid like vinegar would probably eventually result in all of the bleach/chlorine coming out of the material, making the actual answer to Question 1 a 'conditional yes.' However, this is a really bad idea from a health/safety perspective.