India has projected itself for three decades as a bright spot in a tough neighborhood. But 2019 may turn out to be the year it became a trouble spot, depending on the answers to two questions.

First, can Prime Minister Narendra Modi’s Hindu nationalist government preserve India’s pluralistic democracy, or will an urge to settle scores with Muslims produce prolonged strife? Second, can the Indian economy return to the high-growth path many observers had begun to take for granted? In September annualized growth declined for its sixth straight quarter, to 4.5%, down from 7% a year earlier. This is India’s slowest growth since 2013, the year before Mr. Modi’s government was elected.

Under Mr. Modi, India has staked a claim as a “leading power” on the world stage. Its population of 1.3 billion is second only to China. The International Monetary Fund ranks India’s $2.9 trillion economy as the world’s fifth-largest, behind Germany and ahead of the U.K.

Since India began its transition to a market economy in 1991, optimists have likened it to China. Both are vast markets. Their per capita incomes were roughly comparable in 1990. India’s low base and youth bulge—more than 600 million people under 25—allow for rapid growth, in theory, long after an aging China slows. Democracy gives India the kind of deep-rooted stability that one-party China lacks. To smaller Asian nations, India’s success sends a powerful message: You don’t need to choose between prosperity and liberty.

These arguments, embraced by many in Western boardrooms and governments, have spread because they contain an element of truth. But the economic slowdown, coupled with the rise of an aggressive strain of Hindu nationalism, raises another prospect. Instead of becoming a counterweight to China and an engine of global economic growth, India may be headed toward internal instability and economic stagnation.