Muslims in India are a religioud group. there are Tamil Mulims, Kerala Muslims Gujatathi Muslims etc. they are not a homogenous group. A Tamil Muslim has more things commonwith aTamil Hindu or a Christian other than the qusetion of faith ( which is personal) they a common history language culture blood food habbits stc . It is the same with a Kearla Muslim or a Gujarathi Muslim. so it is easy for them to integrate easily with theie local ethnic kin. India at the veery beginning realised unless it is divided into linguistic states it will not survive. This is the the root cause of Inda strength. This is not only in India but in Switzerland Canada, Belgium etc. Countries which tried to forcefully tred to assimilate theor minorities have failed like Ethiopia Rwanda Sudan . More than religion a language and copmmon culture history and customs bids people toghether.
The Tamil SriLanka were never part of the Sinhala polity until the British made both ethe Tamil and Sinhala kingsoms as one country in 1815. As I stated earlier more than 70% of the present day Sinhalses are made up of South Indian Tamils who had gradually come and setteld over the centuries. but they became Sinhalses at their own will. What remains as Tamils are the Tamnils who were never under the Sinhala rule and did not want to become Sihala or Buddhist and forcefully ttying to assimilate them after 2500 years is not going to work. Tamils had a leader like Ghadhi called Chelvanagam .