The correct term is cis, not "female born". Trans women are born female, in the wrong bodies. Cis is the correct term for what you're trying to describe.
And yes, trans women can relate to the problems of cis women, since they confront many of the same issues: unequal pay; misogyny; discrimination; abuse. In the same way cis women are treated as second class citizens, as somehow less than men, trans women experience the same.
Women's rights are women's rights, whether you're cis or trans.