I'm highly skeptical that if antibacterial soap were banned, demand would drive a a black market. People are far more aware of and particular about their Shiraz and Saison (and the intoxicating effects thereof) than their Softsoap's antimicrobial properties.
Liver damage is a person harming themselves by their own choice. Drunk driving is a collection of specific instances of a person breaking the law and taking action which will cause direct harm to another. Alcohol as date rape is just a non sequitur designed to be incendiary. It only effects people who drink and, again, is just a person using alcohol to aid them in committing a crime.
Commonly available antibacterial hand soap hurts everyone even if you are using it reasonably, legally, and responsibly. The harm to the commons is directly proportional to the quantity of it that is used in the normal, reasonable way by everyone.
Alcohol is not great for "society" because it increases the likelihood people will make bad decisions, and can cause specific health problems for the people who choose to use it.
This is akin to emissions standards, which I assume you oppose as well?
Saying you are comparing apples and oranges wouldn't be accurate, because at least apples and oranges are both foods.