Part III of the linked blog demolishes that pretty effectively:

https://acoup.blog/2019/08/29/collections-this-isnt-sparta-p...

TL;DR: Spartan elite women were slightly freer than Athenian women, mostly because all their housework was outsourced to an army of slaves. But they were not citizens, could not choose who to marry, and were by and large treated as property, up to and including lending to other men.

The 95+% of Spartan women who were not in the elite, on the other hand, led lives that were miserable even by the low standards of antiquity, including random rape and murder during the yearly crypteia purges.