Question

why are detergents able to react with both hard water and soft water​

Answer 1

$\huge\bf\mathbb\red{HeyThere!}$

Detergents are used in the case of hard water because the calcium and magnesium salts of detergents are soluble in water.
Soap is less effective in hard water since it reacts to form a calcium or magnesium salt of the organic acid in the soap and forms a grayish soap scum with no lather. Detergents, on the other hand, lather in both hard and soft water.

$\huge\bf\mathfrak{Thanks!}$

Answer 2

Detergent do not react with calcium and magnesium ions present in hard water to form scum.if the water is hard or soft the Detergent give good amount of lather.so it can be able to react with both hard water and soft water.