Why are there religious restrictions on women?
Vedic Dharma for species, castes, and genders is eternal. No one created these rules, so in a sense, one can't answer "why" a particular rule is a rule.
But to make sense of existing rules, the scriptures have given some reasons for why women have more restrictions.
One reason is because being born as a woman is a sinful birth, according to the Bhagavad Gita:
9.32 - O son of Prtha, those who take shelter in Me, though they be of lower
birth [papayoni]: women, vaisyas [merchants], as well as sudras
[workers]-can approach the supreme destination.
And from the Manusmriti:
9.18 - For women there is no dealing with the sacred texts; such is the rule of law; the fact is that, being destitute of organs
and devoid of sacred texts, women are ‘false’.
Mahābhārata (13.40.11-12).—(Same as Manu, but reading ‘Kāścit’ for
‘mantraiḥ,’ and ‘aśāstrāḥ’ for ‘amantrāḥ.’)
Baudhāyana (1.11.7).—‘Women are considered to have no business with
the sacred texts.’
Do. (2.3.56).—‘The Veda declares that women are considered to be
destitute of strength and portion.’
Śukranīti (4.4.9-10).—‘The woman and the Śūdra shall never recite