I am not sure about what other religions say and neither have I read a lot of scriptures of my religion [Hinduism]. I have grown up and see my mother , sister, aunts, grandmother not going to temple or taking part in any religious activity on that particular days. They consider themselves “ Ashaucha” or unclean but I haven’t ever felt any kind of taboo or shame from them. Rather they seem less burdened on those days as they could skip a lot of things from their “To Do” list.
Your post really made me think so I searched on this topic and came up with some good explanations. You can check this one https://www.quora.com/Why-are-Hindu-women-not-allowed-to-enter-prayer-areas-like-temples-while-they-are-menstruating
Hopefully this will help you in some way understanding this social behavior.