Before I answer your question, it should first be noted that there was no concept of "homosexuality" in India prior to (approximately) the nineteenth century. More specifically, there was never an articulated distinction between "homosexuals" and "heterosexuals"; this meant that a man could have romantic or sexual relations with another man, without contradicting his position as husband or patriarch. Women could similarly have relations with other women, without being slotted into an entirely separate category of identity. India also has a fairly long history of what we may call "third gender" or "transgender." It is pretty safe to say that the discourse of "homosexuality" fails to account for the diversity represented by the Indian past.

And there was diversity indeed. Bear in mind that, prior to the arrival of Islam, India (somewhat notoriously) did not have anything comparable to other, more considerable historiographic traditions (like that of China). Many of our early sources, therefore, end up being myths, poems, religious texts, or political and social treatises; none of these necessarily attempted to record life as it was. Regardless, a significant amount has been written recently about the sexual life of India, partly because Western Indologists have been particularly interested with the sensuous and exotic, and partly because of an abundance of material to work with. I'm sure you've heard of the Kamasutra (~300 CE), for instance, which discusses same-sex relationships in considerable detail, and deploys its own set of concepts that don't precisely correlate to our own regarding gender and sex. Perhaps one should not, however, take this as a license to use the text to validate present-day gay sexualities (which Michael J. Sweet notes has been quite common).

Anyway, as Indrani Chatterjee (2012) has noted, in the wake of second wave feminism (so, after the 1960s) scholars began to emphasize the historical variety of Indian sexual arrangements, which appeared to be more diverse, indeterminate, and "fluid" than those of the modern West. Despite undercurrents of orientalist exoticism in the historiography, I find this conclusion to be hard to argue with, as does Chatterjee. Describing the discovery of the Indian sexual archive, she writes,

"A vast literary and aesthetic corpus spoke of adulterous erotic yearnings of mutably gendered beings, of gods who came as ordinary customers to haggle over a courtesan's fees, of the enjoined feminization of all biologically male devotees of Krsna or Siva. iva. Themes of sexual indeterminacy bound eastern Indian Vaisnava poetics from the sixteenth century (Hawley 1988) to their Sufi counterparts in Panjab and the Deccan (Petievich 2007) well into the late eighteenth century."

Chatterjee cites a good number of examples, in case you're interested in reading more (see the bottom for a bibliography). Also note her mention of Sufi poetics -- Islam, by this account, was cleanly incorporated into narratives of India's fluid sexualities.

Shortly after this period of scholarship, historians also began to blame colonial rule for squashing this diversity of sexual possibility, and especially for criminalizing homosexuality. The most significant articulation of this came in the Criminal Tribes Act of 1871, which made it literally criminal to be a "sodomite."

Okay, so how does this relate to your question? First, of all, historians have, at least in recent decades, generally extended the alleged period of sexual fluidity and toleration in India well into the era of Mughal power (~1500 - 1750). Often, they have not viewed Islam as inherently hostile to same sex relationships; if anything, Islamic culture in India has been painted as outright encouraging male homosexuality.

Unfortunately, colonial discourses on the matter of homosexuality are significant in this respect. Europeans in India and elsewhere in the "Islamic world" highlighted a particular practice, which they disapproved of deeply: pederasty, or relations between men and teenage boys. Indeed, the practice of men having romantic or sexual relations with younger, adolescent boys was deeply rooted and extensively represented in Persian and Urdu literature. In particular, the speaker would play the role of a free man who desires a beautiful boy who is idealized as a slave -- thus leading to a poetic reversal when the free man is a "slave" to love (note that the word "slave" had an entirely different meaning compared to English). In this context, the free man is both the initiator and agent of desire (Chatterjee 2002). Since he is active and dominant in the relationship, he can maintain a sense of social position and masculinity; it is for this reason that it was often not frowned upon for powerful Muslim men to engage in pederasty. One famous example is the founder of the Mughal Empire, Babur (d. 1530). In his memoirs, Babur described a young boy whom he came across and feel deeply, madly in love with, and there is little to suggest that he was ashamed of this fact. By this time, narratives of this sort had already become commonplace.

Based on the above we may offer two conclusions: 1) India has largely been characterized by fluidity and diversity in sexual arrangements and 2) Islam in India did not contest that diversity, even furthering it in some instances, for example wrt male same-sex relations. Problem solved? Not quite.

Rosalind O'Hanlon argues, for instance, that the Mughal Emperor Akbar (d. 1605) “made very public efforts to restrain and punish homosexual love amongst prominent nobles”, identifying his court with a heterosexual idiom. In particular, he encouraged a certain austerity in his court, which would deny sexual activity outside of the purposes of reproduction (also see O'Hanlon 1999). Nilanjan Sarkar concurs, pointing out that male same-sex relations disappeared from the archives of the Mughal elite, whereas they had once been commonplace in those of the Delhi Sultanate (~1200-1500). Chatterjee (2002) disagrees, pointing out that Akbar never explicitly objected to "homosexual" relations in themselves, instead seeking to prevent inappropriate power relations between high-ranking nobles and lesser subjects of the empire. I largely agree with this -- nothing about Akbar's sexual politics suggests an antipathy specifically to homosexuality. However, when the Mughal historian Shah Nawaz Khan comments that Akbar found sexual acts between his nobles and younger boys to be "disgusting," no explanation is given. Perhaps Akbar did, in some sense, find same-sex love to be disgusting altogether. On this point, we have no further evidence to work with (to my knowledge).

In any case, Islamic akhlaqi (ethical) literatures, both in India and elsewhere, often commented on sexuality, sexual politics, and related issues. They did, at times, encourage a degree of austerity that would seem to preclude homosexuality altogether. However, to my knowledge there has never been an direct condemnation of male same-sex relationships in the Persianate culture of North India, neither in the 10th century nor in the 18th. Quite to the contrary, Muslims in India produced a huge volume of literature filled to the brim with "homosexual" imagery and metaphors. Whether there was a particular animosity toward female same-sex relationships is beyond me, but I suspect that the sexual controls enacted on women had little to do with homosexuality in particular. For example, there are several recorded instances of noble women in relationships with their eunuch attendants. This was frowned upon (sometimes fatally so for the eunuch), but was, again, not because of fears of sexual identity. At least, certainly not in the sense the term has today.

So how did Muslim rule affect India's views on homosexuality? In one sense, not at all. Islam carried with it new literatures, discourses, and practices, but none of them engaged with "homosexuality" as such. It's therefore hard to say whether society's "view" of homosexuality can change if there is actually no view in the first place. Yes, male same-sex relationships appeared often in the Indo-Persian corpus; in fact, they frequently portrayed the highest forms of romantic passion. But these narratives specifically foregrounded Muslim nobles, and may have had little to do with the lives of most Indians (or most Muslims, for that matter). Even if the Mughal elite depended on heteronormativity to any extent, this would certainly have been irrelevant to all but high ranking courtiers. I am not aware of any recent historian postulating the existence of "heteronormativity" prior to the 16th century, and even after that point the argument remains dubious (see above).

Despite serious gaps in our knowledge presently, I think we can conclude that same-sex love and relationships were common both before and after the advent of Muslim rule. There is, indeed, an abundance of evidence attesting to this fact. They were also apparently common among both Hindus and Muslims, to the point that it seems unnecessary to differentiate too much between the two. I would therefore hesitate to speak of any substantial "change" occurring alongside Muslim rule, other than the kinds of change that always occurs when time passes, people move, and states rise and fall. In other words, there is nothing to suggest that Muslims rulers made any effort to impact the sexual politics of India, which was and continued to be open to diverse sexual arrangements.

I apologize for the meandering structure of the above post. I also have to confess my knowledge of India is rather poor prior to the Mughal period. Please let me know if you have any questions. I'll also be adding a bibliography as a reply to this comment momentarily.