When buying a new automobile battery, how old a battery (according to the manufacture date) would be acceptable?
There is a difference between the date of manufacture and the date a battery is put into service. Many batteries are supplied “dry charged” as this reduces the weight ie no liquid. This is done to reduce transport costs...
Then, they are filled with acid / water mix at the correct concentration and can be used directly or given a “topping up “ charge if necessary.
Well you can always ask the dealer about when was the liquid filled in the battery.
They keep a fair record of it and if not then assuming that battery was filled on the manufacturing date, don't accept old batteries.
Stores don't keep merchandise on the shelf for long these days of lean business practices, so unlikely to find a battery more than a few months old. I would not buy any that required a top-off charge to start the car unless I had no good options.
What kills batteries is the number of charge/discharge cycles (starting the car) and operating in dismal weather (parked outside in the cold). Just sitting on a store shelf won't adversely affect the health of the battery other than the charge will drop slightly. It can always be topped off.