How humans over ages viewed menstruation
Humans knew long ago that menstruation in women and childbearing were related. They had a vague idea of "eggs" in women and fertilizing agent in men (semen). They drew this inference from observing Nature and then extended to humans. Also, they observed menstruation happening in many mammals all around them. What they could not understand was, why it happened so frequently among human females.
The anthropological angle
Anthropologically and philosophically, menstruation gave "birth" to many concepts, ideas and it also moulded social norms. But that is out of context here. The basic idea was, rain falling from the skies made the earth below give rise to plant life. It was not difficult to extend this observation to dividing Natural elements into "male" and "female". Say, earth was female, the gods that made rain possible were male.
That said, not all pre-religion pagan groups were put off by this natural phenomenon of menstruation. The observation that menstruation being related to women's ability to give birth to new humans, made these groups give a new respect to women.
Menstruating women and Hindu Religion
Menstruation is considered unclean & polluting, no doubt. So is the belief in cases of death and also births! And Hinduism is quite fond of categorizing everything into clean vs unclean!
It makes no sense nor is it necessary to search the scriptures for such sanctions. It is a waste of time. Such restrictions may or may not have been official i.e. religious sanction, probably instituted by Brahmin class of yore.
The social angle
Generally a woman in periods got a sort of holiday from her normal back-breaking house-hold chores and as such she would be tired. Possibly, this tradition started among high-caste Hindus just for the purpose of giving the woman some rest. What better way than forbidding her to mix with other members and take part in her usual work? In course of time, this tradition must have hardened into strict isolation where she was not allowed to participate in any religious function or visiting temples.
Thinking about hygiene
Any woman knows the problem of keeping a close watch on the situation. Any strenuous task tends to cause bouts of flow. And the flow is repulsive to see and offensive to smell too. In a large family with many children, there would be a real danger of small kids seeing above unseemly sights. It would make the best sense to keep her in isolation and thereby allow complete rest too.
In the Kamakhya temple of Guwahati, there is an idol of a goddess sitting with both legs drawn up and genitals exposed to full view. Vermilion smeared on the vaginal cleavage represents her menstrual blood. Devotees - male & female - take this kumkum with no hesitation or misgivings at all, knowing fully well that the vermillion symbolizes her menstrual blood. Unless I am mistaken, those days of the lunar month when the principal goddess - Kamakhya Devi - is supposed to be menstruating, are considered particularly auspicious for visiting the temple.
- All this tell us, nobody with any authority can show Hindu scriptures forbidding menstruating women entry into any temple.
- Secondly, this bar appears more a social custom than religion sanction.
- Third, if such a woman enters any temple nowadays, nobody will be any the wiser.
- Fourth, what keeps Hindu menstruating women from entering any temple is simply a feeling of guilt - of violating some norm. Beyond that, the issue is no issue at all.
- There are plenty of female deities in the Hindu pantheon and we attribute all the human characteristics to our deities. This point alone should answer your question!