* Indian-Americans applauded Modi at September rally
* Some of the diaspora now protesting against new law
* Modi's party says overall diaspora support intact
By Nivedita Bhattacharjee and Alexandra Ulmer
BENGALURU/MUMBAI, Jan 27 (Reuters) - Indian Prime Minister Narendra Modi got a thunderous reception when he addressed a crowd of more than 50,000 Indian-Americans in a stadium in the U.S. city of Houston last September.
But four months after the event dubbed "Howdy Modi!," intended to deepen relations with the wealthy Indian-American minority which has influence in India, some members of the diaspora have been protesting against a new citizenship law.
In the past month, small demonstrations from Harvard to San Francisco have underlined criticism of what detractors say are Modi's divisive identity politics.
The law, which was promised by Modi before he was re-elected and was approved in December, in effect granted Indian citizenship to non-Muslim religious groups fleeing persecution from three neighbouring Muslim-majority countries.
Critics say it is a prelude for the marginalisation of Muslims and an affront to India's secular constitution.
"It is still only a minority, but the disenchantment (in the diaspora) is real and deep," said a 50-year-old sociologist who gave her name only as Nidhi to avoid straining relations with older relatives who attended Modi's rally in Houston.
Nidhi emigrated to the United States when she was five and has taken part in demonstrations against the citizenship law in the U.S. state of Texas.
"If we as Indo-Americans don't raise our voice, we are complicit," she said.
The latest protests were outside Indian diplomatic missions on Sunday, India's Republic Day. A large proportion of the rallies attract student, academics and religious minorities -- groups that have long been worried by Modi's rise.
Many in the diaspora cheered Hindu nationalist Modi to an election victory in 2014, convinced he would transform India into an economic powerhouse.
But India's economy has been sputtering because of an ailing banking sector and tepid rural demand, while protests in India, in which at least 25 people have been killed, have revived the specter of social unrest after years of stability under Modi.
Microsoft Corp's India-born CEO, Satya Nadella, told Buzzfeed News this month the citizenship law was "bad."
Even so, a significant chunk of Indians abroad remain die-hard Modi supporters who have staged their own rallies in favour of the law.
Vijay Chauthaiwale, chief of the foreign affairs department of Modi's Bharatiya Janata Party (BJP), said overall diaspora support was intact.
"People believe in the conviction of Mr. Modi. Some transient issue will not affect his popularity," Chauthaiwale said. The BJP has launched a social media push with the diaspora, circulating testimonies from "persecuted minorities in Pakistan" who could benefit from the citizenship law.
But Modi's critics say cracks are appearing in his overseas support.
"Those who are educated are saying, 'Hey, this is not what we were expecting,'" said Sam Pitroda, the opposition Congress party's head of overseas affairs.
Chicago-based Pitroda was unable to provide data, but said he was getting many calls from worried Indians abroad.
Retired engineer Krishna Vavilala, 82, was excited by Modi's rise and recounted being photographed at "Howdy, Modi!" - which took its name from what is a popular greeting in Texas - because his beard made him look like the Indian leader.
But recent developments have given him pause.
He suggested that Modi, who has not answered questions at a press conference in India since coming to power six years ago, speak to more reporters. Vavilala also urged Modi to clarify "perceptions" that he wants to sideline minorities.
"His heart is in the right place," said Vavilala. "But the euphoria of "Howdy, Modi!" has lost its shine." (Writing by Alexandra Ulmer; Editing by Sanjeev Miglani and Timothy Heritage)