I don’t know what religious or irreligious/frei means. (In fact, those terms have no meaning, are irrelevant and should not be utilized.) What I know is that all sources say that the Torah requires a married woman to cover her hair in public. And anyone who didn’t, whether decades ago or today, is most certainly in violation of the Torah.
This kind of answer is exactly why the OP should go and ask his Rav, and not depend on anonymous internet posters who see the world only as black and white without any gray. While you may know halacha, you obviously don’t know how to apply it in real world situations.