Hinduism is patriarchal like most other religions. However, it is also feminist, unlike most other religions. Please note: many Muslim women insist that the Quran for its time gives women unprecedented agency and rights, though social practice of Islam, led by conservative male maulvis, tends to be patriarchal. Likewise, Hinduism contains many feminist ideas that are often ignored, often deliberately, especially by male Hindu leaders and activists who are generally uncomfortable with religion, Hinduism in particular.
Broadly, there are two types of feminism. Equality feminism believes that men and women are equal. Liberation feminism believes that women, like all humans, have a right to make decisions about their bodies, and their lives. Hinduism aligns more to "liberation" feminism than to "equality" feminism.
In fact, equality as an ideology has its roots in Christian mythology that rejected the notion of social hierarchy and saw all men (not women) as equal in the eyes of god. This idea became popular roughly 1,500 years ago when the Roman Empire turned Christian. This idea of equality also informs Islam that all men who visit Mecca are expected to dress in the same uniform, despite belonging to diverse economic, political, national, racial and ethnic groups.
Many contemporary societies want to see people as humans, independent of all biology, including gender. "Equality" feminists seek same opportunities as men. This makes sense when the same labour is involved. Indra has to treat Durga as equal to Shiva or Vishnu if she kills an asura for him. But that does not mean Durga is equal to Shiva, or Shiva is equal to Vishnu. Each one has their unique personality and need. So Shiva is content with raw milk, Vishnu needs processed milk and butter, while Durga demands blood. And "liberation" feminism seeks that diversity to be acknowledged. In feminism, Durga is not inferior to Shiva or Vishnu; nor superior. In "equality" feminism, they are the same, or "as good as" each other. In "liberation" feminism, they are all unique, part of a diverse ecosystem.
In Hinduism, all creatures are equal in the sense that all of them are containers of aatma. However, all creatures are diverse as the aatma occupies different bodies. Aatma is dehi, resident of the body, deha. Everyone’s dehi is the same but our deha is different. So like various plants in the forest, every human is unique, though he or she may belong to a particular species of plant and so display a few categorical commonalities which allows them to be categorised. Categories like be psychological (four-fold varna system of the Veda), physiological (three-fold guna system of Gita), social (thousand communities of the jati system). But the most important category is gender (male, female and others). Just as every plant has different food requirements, different humans need different things. Just as in a garden some plants are favoured over others, in society, some humans are given greater value than others. In some gardens, fruit-bearing trees are valued. In others, flower-bearing trees are valued. Likewise, in some societies, the intellectual is valued, and in others the rich are valued. In some, men are valued, and in others women are valued. Thus, different societies value different aspect of our body.
In Buddhism and Jainism, the female body was considered inferior to the male body. To attain the highest knowledge, one had to take rebirth with a male body. This is because a male body creates life outside itself and a female body creates life inside itself. A male body can retain semen by mind control, however, a female body sheds menstrual blood which is outside mind control.
In Hinduism, a god was seen as incomplete without a goddess. Shiva is incomplete without Shakti, Krishna without Radha, Rama without Sita. Likewise, the householder was seen as a balancing force in society, not the single men or single woman. Single man could be respected if he was celibate; and single woman if she attached herself to a deity like Mirabai, and Andal who loved Krishna, or Akka Mahadevi who loved Shiva.
In early days, both celibate men and women were feared. Celibate men were feared as powerful and fierce yogis with magical powers who could only be controlled and made productive and calm through marriage. Likewise, unattached women were seen as sexual predators and fearful yoginis who could consume men, unless they were restrained by marriage and maternity. This may explain the cultural fear of independent women. The medieval "nath" traditions, the celibate nath-jogi was in constant battle with the wild yoginis and matrikas, who could turn men into goats. Great value was placed on the woman who chose to be faithful to one man (the sati), or who rejected her body altogether, like Karaikal Ammaiyar, the Tamil saint, who became a shrivelled gaunt post-menopausal crone so she did not have to be a wife to her husband and simply worship Shiva without being bothered about her body and its menstrual cycles. In later times, celibate man became holy while unattached single women were seen as dangerous.
Many non-Hindus love to mock Hindus as penis worshippers and see it as reaffirmation of patriarchy. This reveals shame and embarrassment with sexual organs. It also reveals an inability to distinguish between literal and metaphorical meaning of an image. Just as worshipping the crucifix in Christianity is not the same as worshipping a torture instrument, worshipping a lingam is not the same as penis worshipping. In Hinduism, lingam embodies the dehi, while yoni embodies the deha. And so in Shiva temple, you don’t just worship the "penis", you worship the linga placed in a yoni, the union of dehi and deha. Some people call the linga as the male principle and the yoni as female principle. However, this confuses the literal with the metaphorical. In Hindu mythology, the male form or male principle symbolises dehi (spirit or mind) and the female form or female principle symbolises deha (substance or matter). Dehi is beyond gender. Deha is gendered.
This brings us to the yoni or vagina, another word that embarrasses non-Hindus and Hindus who are not familiar with Hindu scriptures. All creatures in this world are classified as yonija, those born of a womb, and a-yonija, those not born of a womb. The former are trapped in samsara, so birth and death. The latter are not. In Ramayana, Rama is yonija and so experiences birth and death like a normal person. However, Sita is not yonija; she is born of earth and so does not die, just returns to earth. Likewise, in Mahabharata, Pandavas are yonija while Draupadi is born of fire so not yonija. Ganesha is a-yonija as he is created outside Parvati’s body. So is Kartikeya. This makes them divine. Yoni or vagina is seen as reminder of human mortality. And so in temples, women are shown standing displaying their vagina to devotees - for it offers both pleasure of life and pain of death. Literally and metaphorically, as symbol of the world. That is why the inner sanctum of the temple is imagined as womb-house or garbha griha and the temple is imagined as a spread-eagled woman who houses the deity in her body.
In Hinduism, all creatures exist within a framework of caste and gender and society, over which one has little or no control. We cannot chose what happens to us; that is determined by karma. But yoga is all about choosing how we choose to react or respond to a situation. We have agency over our choices. We have to take responsibility for the consequences of our actions.
In Manusmriti we are told that a woman is subservient to men: to her father, brother and son. She has to obey him. In other words, her agency is taken away from her. But in Puranas, Sati and Parvati choose their own husbands and Lakshmi leaves Vishnu when she is not treated with respect In Mahabharata, Ganga and Satyavati lay down strict conditions before agreeing to marry. Usha even abducts her lover, Aniruddha, grandson of Krishna in the Bhagavata. In Ramayana, Sita insists she will follow her husband to the forest, despite his opposition. These show that Manusmriti was never "supreme" code as it is made out to be. Women in Hindu narratives have displayed agency in various contexts, in keeping with "liberation" feminism. However, unlike "equality" feminism, you never see Parvati or Sati or Lakshmi or Ganga or Usha or Sita speaking of being oppressed by the men in their lives. There is no victim in Hindu mythology.
Yes, caste Hindus forbade widows from remarrying, but in Ramayana the vanar-queen Tara remarries Sugriva and the rakshasa-queen Mandodari remarries Ravana, tales we don’t highlight as these were practices in "lower" castes. The Vedas have no reference to sati and jauhar that has been glamorised by Bollywood and Rajput communities; but clearly these practices became popular in medieval times. This was part of a global trend towards patriarchy. Yet, simultaneously, in many communities in India, there were women who were allowed to have multiple husbands and lovers, and even inheritance through women. But we do not talk about it as they are seen as "inferior" castes. We must keep in mind that Hindu practices are not just practices of "upper" castes. We must recognise the larger picture of myriad practices. In different communities, and at different times, women had different levels of agency.
Looking at the world through the lens of oppression has its roots in Greek mythology, where the hero is someone who challenges the whims of the gods, who control the fate of humans, and often a martyr who dies resisting. Glamorisation of victimhood comes from Abrahamic mythology where the slaves of Egypt have to be saved by the prophet from the evil Pharoah, or one is continuously asked to mourn the death of Ali, son-in-law of the Prophet. In Hinduism, by contrast, villains whether it is Ravana (who does not care for Sita’s consent) or Duryodhana (who publicly abuses Druapadi) who are seen not as evil, but as ignorant and insecure and faithless. A very different paradigm, one of constant tension, not vilification. In Hinduism, God is not a judge and so feminism is not about judging men.
To deny a person, male or female, agency is to indulge our ego (aham); it is an outcome of insecurity that makes us want to control and dominate. A wise man or woman will always grant agency as per their level of self-realisation (atma-gyan) so that the dehi can experience life to the fullest through the deha, be it male or female. This essentially is the idea that would inform Hindu feminism.