I am a bit surprised, Professor Volokh, that you have dared to wade into India's murky politico-religious scene! Accusations and counter-accusations of which administration is more communal than another is as commonplace - and often devoid of logic - in India, as which administration is more racist than another in the USA.
If you are familiar with identity politics in India as I am, there is not much insight to be gained from this article. If you are not - as you admit - then you are only getting half of the story. To get a flavor of “how liberal” communists — even India’s communists — are", please read this: "Editor arrested for 'outraging Muslims". You may also research similar incidents relating to Sanal Edamaruku, Taslima Nasreen, Salman Rushdie ... during the previous administrations, mostly of the Congress Party.
Looking beyond these political shenanigans, the legal scene regarding freedom of speech in India is, and has been, quite dismal. Ostensibly, freedom of speech is guaranteed under Article 19 of the India Constitution. This article has been amended, claused, and subclaused so much, however, that it has been rendered meaningless. As Justice Scalia said during a a Senate Hearing in 2011, ".. it’s just words on paper, what our Framers would have called a “parchment guarantee.”"
Section 295 A of the Indian Penal Code, for example, reads: "Whoever, with deliberate and malicious intention of outraging the religious feelings of any class of citizens of India, by words, either spoken or written, or by signs or by visible representations or otherwise, insults or attempts to insult the religion or the religious beliefs of that class, shall be punished with imprisonment of either description for a term which may extend to three years, or with fine, or with both." This is essentially a blasphemy law that has been enforced selectively across administrations to score political points. A summary of the legislative and case history of 295A can be found here.
Another example, Section 66A of India's IT Act which extends 295A to all communication including electronic communication, is a death knell to any semblance of freedom of speech. I am sure that the author of the New York Times article is aware that the said amendment was passed by the ex-Prime Minister Manmohan Singh and the Congress Party, 6 years before Prime Minister Narendra Modi and his party, the BJP, took office in 2014.
Regarding the three murders in particular referred to by the author, while they could well have been perpetrated by Hindu extremists, and I personally suspect so, to the best of my knowledge, no one has been apprehended or convicted so far. Further, at least in one case, family dispute is suspected by the police, and that's in the Congress Party governed state of Karnataka. It is worth noting here that these murders are preceded by years, even centuries of religious violence and mayhem in India.
Concluding from a few such recent incidents that "the country is undergoing a tectonic shift that will have long-term repercussions", is similar to concluding that a tectonic shift is occurring in the USA, after reading that Mike Huckabee and Ted Cruz had visited Kim Davis in prison. Or, because a random guy with a history of mental illness and subscribing to a potpourri of extremist ideas went on a shooting rampage in Oregon.