The frontrunner to be India's next prime minister after elections in May is Narendra Modi of the opposition Bharatiya Janata Party, so it's time to consider what his leadership means for his party. Can the BJP fill a vacuum in Indian politics by becoming a modern right-of-center party that stands for both sensible pro-market policies and openness to Indians of all faiths? A lot rides on the answer.
For India to regain its economic luster, it must reassure skittish investors that it isn't doomed to be governed only by fiscally reckless populists. As for the BJP, after ruling India for only six of 67 years since independence, the party needs to evolve as a credible alternative to the left-of-center Congress Party—one that can represent all Indians, not just Hindu nationalists. This requires reassuring voters that the party can rein in a hateful fringe that stands for book banning, minority-bashing and conspiracy theories.
So far the prognosis is mixed. By rolling out a red carpet for business in Gujarat, where he is chief minister, Mr. Modi augurs a BJP that has outgrown a traditionalist wing long mistrustful of capitalism. He has put into action the modernization of economic thought needed by a party that has long included powerful forces more comfortable with import substitution and small-scale industry.
But Mr. Modi has yet to quiet fears that his ascent suggests a party becoming less tolerant. For his detractors, Mr. Modi is indelibly associated with the 2002 anti-Muslim riots that erupted after a Muslim mob torched a train carriage filled with Hindu pilgrims in Gujarat. More than 1,000 people died in the violence, three-fourths of them Muslim. In December, a court upheld a Supreme Court-ordered investigation that cleared Mr. Modi of legal culpability for the riots. But for much of India's 150 million-strong Muslim population, Mr. Modi's name remains mud.
The candidate has tried to cultivate a reputation as an icon of administrative efficiency and personal probity. He has cracked down on Hindu extremists in Gujarat guilty of breaking the law. In a landmark speech in the northern city of Patna in October, he declared that poor Hindus and Muslims should unite to fight their common enemy—poverty. His campaign eschews the Muslim-baiting that accompanied the BJP's rise to prominence in the 1990s.
But while Mr. Modi may have tacked toward the moderate center on interreligious matters, you can't say the same for his party. The BJP remains an outfit where minority baiting is more likely to earn commendation than reprimand. Party MP Varun Gandhi, caught on tape using unprintable epithets to describe Muslims in 2009, has since been promoted to general secretary. Last year the party admitted Subramanian Swamy, a former minister who wants to disenfranchise Muslims who deny Hindu ancestry, and who demands that Muslims publicly apologize for the alleged crimes of their forebears.
Every party in the world has its share of cranks, but respectable parties don't generally make them leaders or allow them to spout off regularly on national television. If you ask party moderates about these egregious choices, they either justify them based on short-term tactical calculations or point to other parties that pander to Muslim extremists. Outsiders tend to ascribe the problem to the Hindu nationalist volunteer group Rashtriya Swayamsevak Sangh, which provides the BJP with much of its leadership and many of its most committed cadres. (Mr. Modi began his career as an RSS volunteer.)
Whatever the reason, this comfort with Hindu society's lunatic fringe has hurt the BJP disproportionately. It nudges talented Indians with no particular socialist bent—but also no particular hatred of Islam or Christianity—toward the Congress Party or the brand new Aam Aadmi (Common Man) Party. The result: a continued leftist tilt among India's educated elites.
How might Mr. Modi prove the skeptics wrong? He can start by reaching out to talented Muslims, Christians and Parsis who share his economic ideas. (In 2009, the BJP selected only three Muslim candidates to run for Parliament; Congress picked 29.) Mr. Modi can refuse to share platforms with hotheads and lean more on moderates such as the urbane leader of the opposition in the upper house of Parliament, Arun Jaitley, and Goa Chief Minister Manohar Parrikar.
As Mr. Modi ramps up his campaign, it may be unrealistic to expect him to address this problem directly just yet. But sooner or later he will have to confront the extremists within his fold. By embracing modern economic ideas and tempering his own rhetoric toward Muslims, he has begun the slow process of transforming the BJP into a modern conservative party. But as long as it remains tolerant of intolerance in its midst, it will never become a mainstream alternative to Congress.
Mr. Dhume is a resident fellow at the American Enterprise Institute and a columnist for WSJ.com. He is on Twitter @dhume.