Coffee, it’s simple; we have a mesorah.
The sams gemara in sotah 22a contains an important yesod. It says that a person who is קרא ושנה, learned tanach and shas, but did not have a rebbe from whom he received a mesorah, is called an am haaretz. Says rav Hirsch, such a person might know halacha, but he won’t be able to tell when and how to apply various values in avodas Hashem and mussar.
This is why the mishnah says “lo am haaretz chosid” and not the seemingly more appropriate “lo am haaretz tzadik,” as a chosid is someone who goes beyond halacha, while a tzadik keeps the dinim; asks Rav Hirsch, why would a traditional am haaretz not he able to be a chosid – it should say tzadik! Since he doesn’t know halacha. Answers rav hirsch, we’re talking about the above.
That particular woman had zchusim, and in context, it was to show that not all women who daven a lot are immoral(a lot are, the gemara says, because they’re trying to hide their sinfulness).
But the gemara is not saying what a woman *should* do, just that she has more schar for walking, and that principle applies to a man as well, as codified in shu”a.
It’s not an ikkar for women to go to shul. They’re not going to be taken to task for it; most rebbetzin hardly ever go, especially by the litvishe. First things first; work on the basics of tznius in dreas, attitude and behavior, not being an azus panin, work on chessed, jealousy, lashon hora. A woman – and a man – have lifelong battles to work on before they begin taking on extras. Shul for a woman is like tikun chatzos for a man; great thing, but rather silly if he’s not able to keep the basics yet.