That's not culture so much as it is the side effect of culture merged with their current development state as a country. That is, if India's quality of living and development were advanced to that of the west, there probably wouldn't be anything objectively inferior culture-wise.
It is definitely culture. The US didn't start treating women reasonably on its own. It required a generation of women to protest in the streets until the culture and the law changed. This hasn't happened in India yet, but is hopefully now beginning. I wouldn't draw too many direct parallels between women in the pre-'60s US, and women in India since the respective traditions are so hugely different, but what has to happen to fix it is the same.
What I'm going to describe is a bit of a caricature, but it's true enough that it's the dominant theme of Indian soap operas. Traditionally in north India, women don't even eat with the rest of the family. They are expected to remain in the kitchen cooking and serving food until the meal is finished, when they eat whatever is left, alone. The woman only gains power in the family when she's the oldest person left alive, at which point the veneration for elders supersedes her subjugation. The stereotype is that at this point, she takes out the frustration of her years of abuse by ordering around her daughter-in-law.
But I still think it is societal development. Liberalism is a natural evolution as the quality of life and the society advances, and so the way woman are treated in India I believe is an effect of its development, not an effect of its culture.
Like you said, the US had the same stage. We used to be heavily racist and also oppressed women during an earlier stage of socio-economic development.
I don't think it's a useful model to suppose that there's some underlying "true culture" that doesn't change over time and that will be gradually revealed as their economy improves. Culture changes, and economic development is a catalyst for change. Whatever way people behave today, that is the culture today, and if they behave differently tomorrow, that will be the culture tomorrow. Right now, Indian culture subjugates women. In the future, it hopefully won't.
Liberalism might be an "inevitable" consequence of advancement from one stage to the next, but real people have to fight for it to make it inevitable. When they fight for it, they will be changing the culture, not revealing it in a more true form.
