Some religions encourage, both men and women, to shave off their pubic hair and anus hair.
What does Sanatana Dharma say to its followers about this?
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There is no instruction that the hairs on those parts should be shaved off.
In fact we have the following verse:
Manu Smriti 4.144. Except when sick he must not touch the cavities (of the body) without a reason, and he must avoid (to touch) the hair on the secret (parts)
So, it is quite clear that there is no rule that the hairs on those parts should be removed.
But, where it is a question of performing penances (for atoning for some sins that one has committed), several scriptures recommend shaving off hairs from all over the body. Because according Hindu scriptures sins are stored in the hairs.
For example, we have:
If the foetus of a cow is destroyed, while it is in an amorphous state, a quarter penance is prescribed for the sin; when it has attained some distinct form, then the penance should be two quarters ; by destroying a foetus which has not yet developed its consciousness, the sinner must perform three quarters.
In a quarter penance, the rule is to shave the hair all over the limbs ; in two quarters, the beard likewise ; in three quarters, the shaving is to be of all hair, except the coronal lock; but on killing after birth, the shaving includes the coronal lock too.
Parashara Smriti Chapter 9
But, that's only while engaging in a Prayaschitta. In ordinary circumstances there are no specific instructions.