Like a lot of novels I have loved, this one requires patience and persistence. It is decidedly worth the effort. My impression of the negative reviews for TMoUH is that the reviewers chose not to expend the necessary effort.
Non-Desi readers unfamiliar with the culture of post-independence India will find some of the vocabulary baffling—and I don't refer here to the brief passages of Hindi, Urdu, Punjabi, etc., which the author kindly translates into English for us. Roy sprinkles in words like tiffin, not widely known in the Americas, and leaves it to the reader to figure out their meanings from context. It can be alienating to readers not willing to step outside their own Euro-American cultural boxes.
As it is, the India that Roy paints for us is so different from the US that the story may as well take place on another planet. The book itself may as well be stocked in the Science Fiction section of your local book emporium. It probably doesn't help that the first part of the story involves a character's (Anjum's) transition from boy to hijra, who switches gender presentation at convenient times like a character from Ursula LeGuin's The Left Hand of Darkness.
On top of that, Roy takes pains to remind us that India is a big place with many cultures: there are differences in lifestyle not just among Muslim, Hindu, Sikh, Christian, and secular, but also among various states and regions. They don't do things in Kerala the way they do in Kashmir or Andra Pradesh.
Those unwilling or unable to surrender to the strangeness of the setting, to be transported by its mysteries, will miss out on Roy's use of language, the ways she combines words, which is dazzling and other-worldly in itself.
It was very ambitious of Roy to pack into 500 pages so much of India's 70 years as a nation: e.g., the chronic military inflammation in Kashmir, the aftermath of the Bhopal explosion, the rise of Hindu nationalism, the persistence of the caste system in a supposed democracy, relentless urban expansion and gentrification, and various manifestations of religious persecution. I still cannot decide whether she was a bit too ambitious: These historical details make for a richly-backgrounded story, but it seems to me that the character development suffers as a result.
Most problematic for me is Tilo, or S. Tilottama. What is it about her that makes the men in her life fall so recklessly in love with her? She doesn't exhibit any truly endearing traits. She smokes tobacco and cannabis, she drinks hard liquor, she's sexually available, but she doesn't seem to derive joy from any of that. She appears for a while, takes what she needs, and moves on. Is it that she has the audacity to shed tradition, to live as a modern woman? Fortunately, she also provides the closest thing this story has to a resolution, when she finds her true purpose and a community that accepts her.
There are also characters who disappear from the narrative for several chapters, not yet having made much of an impression, only to return. The reader is left to wonder, "Wait—who's this again? To whom is she related, and how?"
Roy does not make it easy for the reader to keep track of what time period a certain chapter occupies. I can easily forgive that: She is writing about a place still emerging from traditional society with a perspective of time that is cyclical rather than linear. Time is also fluid and somewhat illusory.
Character issues aside, my favorite aspect is the persistent theme of individuals and groups adopting lost children, adults, and animals. They form families of choice, with relationships that transcend linguistic and religious boundaries. In this universe of cruelty—sometimes random, sometimes targeted—Roy implies that the best hope of our species lies in embracing diversity and building intentional communities like the one Anjum has founded in a Delhi graveyard.