Cloths can be used ... were used for most of history. (I was told by American Indians in Oklahoma that they traditionally used cattail fluff to make a type of disposable diaper-stuffing. I wonder if they made something similar for menstrual use.)
There is a confluence of negative factors in the situation described in India. Poverty and low technology, yes, but also a cultural effort to entirely hide women’s menstruation from general knowledge, as part of a more general rock-bottom status of women. (The inventor didn’t know such a thing existed until he got married!)
The difficulty of accessing water seems to be complicated by an effort to restrain and isolate women. They can’t hang the cloths to dry, because that would be admitting they exist!
Under other circumstances, the use of absorbent cloths for menstruation is uncomplicated. From a practical standpoint, it’s just like using cloth diapers, but not as smelly. Rinse out, soak, scrub and bleach (if possible, not essential), and dry in the sun.
The trouble in India stems directly from poor private property rights and socialism.