So are you saying that a Jewish married woman who does not cover her hair is irreligious? Hmmmn, a lot of those women are supporting YOUR Yeshivos. And Litvishe K”Y, I know the halacha. Not ALL sources agree, though it is clear that most do. There are well-known frum women who did not cover their hair decades ago. No one would dare to suggest they were not frum.
I personally cover my hair publicly and privately. That does not mean that the Shomer Shabbos, Kosher, mikvah-going woman who lives next door to me is frei. And if you believe she is, it speaks to an issue that is far more egregious than covering or not covering one’s hair.