This question makes a few assumptions that make it difficult to answer.

"Indian culture" is exceptionally diverse, and Indian history especially so. When we speak of historical India, we're talking about an area from about what is now Afghanistan to what is now Burma, and from the Himalayan Mountains to the Indian Ocean. India is a modern nation state that only came into existence in 1947. Prior to this what is now India was largely colonized by the British, along with smaller Portuguese and French colonies. And prior to that India was largely divided among a multitude of kingdoms and dynasties, both large and small throughout its 5,000+ year history. Before British colonization, anything close to a unified India under one kingdom only happened a few times; namely under Asoka, the Delhi Sultanate and the Mughals. Also, parts of historical India are now other countries like Nepal, Pakistan, and Bangladesh.

Hinduism is also an especially diverse religion in terms of beliefs and practices. There are different schools of thought in Hinduism and Hindus are far from homogeneous in their beliefs and practices. Several different religions originated in India, including Hinduism, Jainism, Buddhism, and Sikhism. India is also now home to local populations of almost every religious group in the world. The Kama Sutra wasn't solely about sex, it was more so a guide to righteous and meaningful living. The idea of sexual purity and mores is certainly present in Hinduism and other religions originating in India. In addition to what we find in Hinduism with the Kama Sutra, we also see things like Brahmacharya. Like with the Kama Sutra, Brahmacharya is about more than sex, but includes ideas about the practice of celibacy and sexual purity. Brahmacharya is found in the Vedas which are thousands of years old.

It is also very precipitous to start to label things in terms of "repressed" and "liberal," they are relative terms and culturally located. Therefore it is very difficult to speak of Indian culture and history in sweeping terms, especially labeling things in this way. There is no doubt that ideas surrounding sexuality have changed in Indian cultures throughout history. Some of changes might have come from "outsiders," like other posters might suggest, but Indian history and culture has always been dynamic, diverse and difficult to label in modern terminology.

As a secondary question, I would love to know if there are any efforts to reverse this and if they're connected to that previous heritage or new ones.

Also in addition to that question, how much of an influence did the Mughal Empire have in comparison to the British empire in shaping the eventual conservative perspective on sexuality in modern India ?

I think this is a question more for /r/sociology. Sexuality culture is just too complicated for a simple historical analysis like that. For example, the modern culture in the USA includes both widespread abstinence only sex education and promise rings in public schools and the popularity of Dan Savage and the ubiquity of Internet pornography, and that is a single time period for a unified country, not millennia of a politically diverse geographical area.