During menstruation, why are women not allowed to touch anything related to God or be involved in any religious activity?

Back in those days, everyone bathed at the village pond/bathing spot in the river, and a location a little farther away was used as potable water source as well as for washing clothes. When menstruating women bathed in these waters, the bloody discharge increased the iron content of the water. This in turn attracted iron loving bacteria, increasing their numbers significantly in the water. The problem with iron bacteria is they tend to make the water brown and slimy, unfit for drinking and stain any clothes washed in this water. 


Therefore, women were prohibited from bathing in these waters when they were menstruating most heavily, which is typically days 1 through 3. As a result, they were literally dirty and unclean from not bathing for so long, especially in Indian weather, and were therefore not permitted in the kitchen or at the altar without bathing. Sleeping without showering for 3 days will obviously result in dirty sheets, hence the required washing on the same day the woman gets to take a bath.

This reason stopped being valid a long time ago with the advent of private bathrooms and plumbing. However, old habits die hard and along the way, the original rationale was forgotten. What we are left with today is blind adherence to "tradition" minus the understanding, hence the anachronism.

EDIT: This in response to some of the comments and other answers supposedly in response to mine that impute meaning to my words that were never intended.

1. The answer is specific to the question. I don't know which Shastras because my 13 year old self didn't think to ask my grandfather for the source and by the time it occurred to me in my twenties, my grandfather had passed away. So yes, it's what one man told me and I have plenty of reasons to believe him. Notice that I didn't say you should. Feel free to believe what you will, you don't need my permission. And no, I am not going to prove Shastras existed.

2. I merely offered a literal retelling of what I was told. None of this is *my* opinion masquerading as facts. Here are other things it's not:
- a defense of patriarchy
- a defense of senseless traditions
- some Hindu superiority agenda
- some Hindu inferiority agenda
Or anything else you inferred that I have not explicitly said.

3. I don't know whether they knew about microbes, whether the Shastra predates knowledge of microbes or vice versa, how big the body of water was when they observed this, the rate of flow, whether all Indians lived next to rivers when the Shastra was written or why they didn't pursue alternate options like transporting the water elsewhere to have a bath. If I wrote the Shastra, I could have told you. 

It makes perfect rational sense to me in the case of small bodies of water like a temple pond where people did draw drinking water from, and washed the deities' clothes if not some of theirs. If it doesn't make sense to you, no worries, c'est la vie. Like I said elsewhere, in science, much depends on the assumptions