Nikhil Menon, assistant professor of history at University of Notre Dame, says:
An Indian citizen cannot hold dual citizenship: this dates back to rules determined by the constitution of India, passed in 1950, and a citizenship law from 1955. The recent allegation that Rahul Gandhi is a British citizen, and therefore not Indian, should be seen as a way of delegitimizing an opponent (similar to Donald Trump's birther charge that President Obama wasn't born in the U.S).
Mr. Gandhi's Italian-born mother, Sonia Gandhi, has also long faced political attacks over her citizenship, especially during the 2004 general elections when she was expected to become Prime Minister.
The reason this is a reliably effective rhetorical strategy for opponents of the Congress party is because, regardless of its veracity, it lets the theme of divided loyalties and financial privilege hang in the air during an election.
It contributes to the BJP's narrative of Rahul Gandhi as a rich dynast with dubious foreign connections, marking a stark contrast with Prime Minister's Narendra Modi's image as an austere son of the soil.