This is very accepted (that girls / women in the Chassidisheh circles do not fast) based on the folloing premise:
They are either:
too young to fast (and it might hurt their future productivity)
too old to fast
they are expecting / nurshing (or soon will be)
Everyone (according to the chassidisheh mindset) falls into one of the above 3 categories, so aside from Tisha B’Av, Yom Kippur (and in some households, Taanis Ester), women do not fast