Does reaction of alkali and alkaine earth metals' reaction with water an acid-base reaction?
Na and K react with the O-H bond of the water molecule. This removes the H atom that is reduced to an H atom and then to a H2 molecule. It is not an acid/base reaction. It is a redox reaction. Na or K atom is oxidized at the end. No metal oxides are produced as intermediating state.

Alkaline and alkaline earth metals act in the same way.