In New England, being an “independent woman” means you graduated from one of the Seven Sisters and still go to reunions, took more than one course in “Women’s Studies”, smoke cigars, teach or work for a nonprofit, live with cats or if you got married (to a man) you kept your last name and plan to hyphenate the name of the in vitro baby you will bear as you approach 40 - or 50
I learned a new word (for me - the usage is actually quite old) this weekend that seems to apply here: bluestocking. Eleanor Roosevelt was one, in her day. I think it fits.