Whether American Muslims’ optimism will ultimately prove to be warranted rests on whether they follow the pattern of making close personal connections to Americans of other religious backgrounds. Indeed, the same is true for all of America’s many religions—large or small.

What’s the path to religious acceptance in America—and what can Muslims, Mormons and Buddhists learn from Jews and Catholics?

A Gallup report out last week found that, of all major religious groups in America, Muslims are the most optimistic about their future. When asked what they think their lives will be like in five years, Muslims see themselves as having a better life than do members of any other religious group. They are also most likely to say that their community is getting better as a place to live.

Why is such optimism warranted even though Muslims are also the religious group most likely to report experiencing discrimination?

Consider the experience of two groups that are perceived positively by Americans today: Jews and Catholics. Americans rate Jews and Catholics more warmly than they do mainline Protestants, historically America’s religious establishment, and evangelical Protestants, the single largest religious group in the country. At the end of the scale opposite Jews and Catholics are Muslims, Mormons and Buddhists.

There was once a time when Jews and Catholics faced greater hostility than Muslims (and certainly Mormons and Buddhists) do today, even including mob violence. The accusations commonly leveled against Jews and Catholics—all the way up to the 1960s—should sound familiar. Among other things, their religions were said to be incompatible with America’s democratic system of government, their adherents beholden to foreign influences.

Mr. Campbell is an associate professor of political science and director of the Rooney Center at the University of Notre Dame. Mr. Putnam is professor of public policy at Harvard University. They are co-authors of “American Grace: How Religion Divides and Unites Us” (Simon & Schuster, 2010).

[Editor’s note: This article is incomplete. The source for this document was originally published on online.wsj.com—however, the original URL is no longer available.]