Beer is made ___ yeast, water, hops, and malted barley

Of and out of both carry a slight implication that the beer is simply assembled from those ingredients, rather than crafted.

With, as you yourself hinted, implies that the listed ingredients are not the only - or even most important - components.

From, therefore, seems to be the logical choice. That being said, the differences are very slight, and I doubt that anyone would correct you for choosing any of the others.

to brew is the verb usually associated with beer:

To make (ale or beer) from malt and hops by infusion, boiling, and fermentation.

The process of brewing beer.

Dorothy Sayers' Murder Must Advertise has a lovely paragraph where an advertising executive learns that he may not legally say cider was made from apples unless it has no other components, nor out of apples unless it is mainly apple juice, but fortunately he can say it was made with apples even if most of it comes from turnips. So which is "correct" depends both on how the beer was actually made and on how you wish to imply it was made.

(Note to eager advertising executives and lawyers: though Sayers' research was impeccable, it was in Britain some eighty years ago.)

Beer is made from...

New Oxford American Dictionary provides a definition that fits the exact context:

from (preposition): 6) indicating the raw material out of which something is manufactured

Of works but has (to me) a hint of that you couldn't be bothered to find a more specific word.

From is best, and only weakly implies an exhaustive list. "Beer is made from (among other ingredients) malt and hops" is perfectly sensible with or without brackets. Especially as water is a rather obvious ingredient.

With is just too vague - it could even be taken to mean "in the same factory as", e.g. "beer is made with cider in a brewery" (UK meaning of cider).

Out of has the flaws of of but a stronger suggestion of exclusivity.

Strictly speaking beer is brewed from malted barley and water, using yeast, and only flavoured with hops, however it would seem sensible to ignore this distinction as the hops are fundamental to beer. The yeast is not an ingredient in the cooking sense - it takes an active part in the process.