There are different definitions of acid and base (Lewis, Bronsted-Lowrey etc) and it gets all the more complicated in biochemical situations. In a nutshell the acidic or basic properties of the food you eat are down to the mineral ions (in this instance), not really the H+ or OH- you usually see in acid alkali chemistry. These acid and basic properties of the food you eat are not apparent until they are metabolised and the acid/base chemical properties of the foods are unlocked.
For example lemon juice tastes sour as it’s an organic acid. It contains three groups called carboxyl groups, which will readily react in an acidic fashion (due to H+ ions breaking off the carboxyl group) so the acidity is readily apparent or ‘at the surface’ if you will. That acidicty is dealt with long before it reaches the kidneys. Remeber the stomach is a bag of acid.
The acidity in meat is hidden on the other hand, its physiologically acidic properties are locked away in the structure of the tissues. As it’s digested, utilised by the body then eliminated from the cell as waste, then the acidic properties come out of the woodwork and have to be dealt with.