Goa was colonized by the Portuguese. The local cuisine has elements of Portuguese culture for instance one of the most famous curries Vindaloo is inspired by the Portuguese dish "
carne de vinha d'alhos".
India has one state Nagaland which has a separate flag and a Christian majority. Christianity had some influence over the Indian culture but it's still not as influential as Hinduism, Buddhism, Sikhism, Islam or Jainism. Indians are proud of their culture. The British weren't like the Roman Catholic Church who tried to subjugate the masses by using religion. They were secularists who tried to promote secularists values wherever they went. Still, there is a kind of slave mentality in Indians, Bengalis and Pakistanis where we feel we have to dress and act more white to be taken seriously.
Regardless, the birth rates are starting to fall in India too. There is this thing in economics called the demographic cycle. According to the demographic cycle when countries start to become rich and women become more educated in a country the birth rates start to fall. This has nothing to do with any religion.
Even if it did, I personally don't think there is anything wrong with a person being pro-life and deciding not to try birth control methods. There are some people who have more children because this is what they desire not because they are indoctrinated by a religion. The government shouldn't put restriction on the number of children a family can have. Having children is a parental right. When they introduced one-child policy in China people were forced to kill their own children. Later, people started to engage in female infanticide. The reason is because in China the laws say that a son is obligated to look after his parents when they become old. However, the daughter has no such obligations. Chinese families killed girls because they were worried they would have no one to look after them in their old age. It was wrong and many thousands of young girls died because of just one disasterous policy.
Everyone likes to scapegoat religious people but the truth is most people who everyone thinks are "religious" aren't actually religious at all. I will say as a Muslim there are families where the men and women pretend to be religious. They pray five times a day and are constantly mentioning God but then these same people take bribes, lie, cheat and engage in backbiting. Most people treat religion like culture. Just because everyone is doing something they will follow. These so called religious people are quick to leave their religion and become atheist or agnostic when there are changes in their culture that push for anti-religious narratives.