As our resident chemist I should probably chime in here.
Good advice about NOT ever combining bleach with any other cleaner. If you combine it with ammonia you make not chlorine gas (as is incorrectly but commonly assumed) but rather chloramine gas. Doesn't make much difference what you call it though, as you will be just as dead. My own wife did this one time and I had to rush her outside to get some fresh air.
I've not ever heard of vinegar - which is quite dilute acetic acid - hurting aluminum. In fact, a common suggestion for removing the discoloration of aluminum cookware after it is sometimes darkened by washing with harsh detergent is to boil water and vinegar in the pot. But I would not do this for long, as it can eventually pit the surface.
The problem with bleach and aluminum is not the bleach part but rather the alkalinity. Bleach (sodium hypochlorite) is not only a strong oxidizer, but pretty darn basic, meaning it's like adding lye, or strong base such as sodium hydroxide. And in case you didn't know, the bubbling action in traditional Drano drain cleaner comes from the reaction of powdered aluminum with sodium hydroxide. So if you put an aluminum part in strong alkali (such as bleach) for long enough the whole dang thing will dissolve. (I saw this happen one time back in graduate school - very embarrassing.)
And as mentioned, the thing about bleach in aluminum tanks is that it is OK to use a few capfuls on a normal basis, and maybe even a couple of cups for a BRIEF shock treatment - but do not go pouring a gallon of bleach into an aluminum tank and leave it overnight. You can get away with that (even if it is overkill) with a poly tank, but the aluminum tank will eventually pit right through.