Even if that were how it worked, which it isn’t, that would still be horrible for your body. The body doesn’t want to be neutral, it wants to be stable, and that’s not quite the same. For instance, blood pH hovers around 7.4. If it becomes neutral (which is 7 on the pH scale), you would die. In fact, if it even goes as low as 7.34 or as high as 7.46, you would probably die. The same is true in your stomach. It contains HCl (hydochloric acid), which is a strong base, to digest your food. It has a bit larger of a range, but it still stays between 1.5 and 3.5. If it goes too high, you can have some serious digestive problems.
Chemistry of stuff doesn’t depend on just acidity and basicity. When you’re dealing with things like HCl and NaOH then they ‘cancel out’ since you’re left with H2O and NaCl at the end, but the salt isn’t necessarily harmless.
A common soap product is sodium laureth sulfate, which is already a salt (hence the sodium); it’s produced as sulfate-containing compound (-SO3H), an acid that is then neutralized. So by the time you’re encountering it, it’s already in a salt form.
TL;DR: salts aren’t guaranteed to be safe. The salt-form compound can still be harmful to you. Even though the acidic or basic part of a molecule is neutralized, the rest of the molecule can still have effects.
To test your hypothesis, try drinking a mixture of hydrochloric acid, and bleach (which is an alkaline). Repeat the process and adjust the quantities of each until it tastes just like water.
(please don’t do this – but hopefully you get my point, just because it is acid/alkali/neutral, doesn’t mean you can consume it).
A few things here:
1. Strong detergents like concentrated laundry pods are basic to the point that you could get chemical burns in your throat and mouth before the soap even made it to your stomach. So that’s bad.
2. Just because acid and bases “cancel each other out” doesn’t mean you want that to happen. Your stomach is acidic for a reason. Your body tries to keep the various environments in your organs in relatively stable condition, including pH. Your body can handle mild disruptions, but large changes take a toll on your body while it tries to return to normal conditions, and could even cause immediate damage. Your cells like the pH they live in, you shouldn’t try to change that.
3. There are lots of chemicals in soaps, like fragrances, dyes, solvents, surfactants, etc. They aren’t meant for human consumption, they are meant to clean things. Possibly sanitize things. And sanitizers aren’t usually picky about what they’re sanitizing. They’ll kill your human cells just as happily as germs.
The atoms don’t stop existing just because the molecules are acidic and basic, and most soaps aren’t entirely bases; the results of mixing an acid and a base is water + some sort of salt + any leftover material which didn’t match up. You could potentially leave a whole lot of chlorine just hanging out if you mix the wrong acid and bases. Not usually the kind you find in soaps, but who knows what those might leave behind.
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