If you haven't read Justice Kagan's dissent to the Supreme Court's pro-governmental-prayer decision in Town of Greece v. Galloway, you should. Here's a taste: 

Let’s say that a Muslim citizen of Greece goes before the Board to share her views on policy or request some permit... But just before she gets to say her piece, a minister deputized by the Town asks her to pray “in the name of God’s only son Jesus Christ.” App. 99a.

She must think—it is hardly paranoia, but only the truth—that Christian worship has become entwined with local governance. And now she faces a choice—to pray alongside the majority as one of that group or somehow to register her deeply felt difference. She is a strong person, but that is no easy call—especially given that the room is small and her every action (or inaction) will be noticed. She does not wish to be rude to her neighbors, nor does she wish to aggravate the Board members whom she will soon be trying to persuade.

Justice Kennedy's majority opinion, on the other hand, repeatedly takes a tone of "eh, non-Christians can probably handle it":

Our tradition assumes that adult citizens, firm in their own beliefs, can tolerate and perhaps appreciate a ceremonial prayer delivered by a person of a different faith. See Letter from John Adams to Abi­gail Adams (Sept. 16, 1774), in C. Adams, Familiar Letters of John Adams and His Wife Abigail Adams, During the Revolution 37–38 (1876). The prayers delivered in the town of Greece do not fall outside the tradition this Court has recognized….

It is presumed that the reasonable observer is acquainted with this tradition [of legislative prayer] and understands that its purposes are to lend gravity to public proceedings and to acknowledge the place religion holds in the lives of many private citi­zens, not to afford government an opportunity to proselyt­ize or force truant constituents into the pews. 

That's a lot to assume/be presumed: people know what they believe, don't mind hearing what someone from a different (read: dominant) faith has to say in a prayer over a body that governs them both, and are acquainted with the tradition of legislative prayer in the U.S. and what its purposes are and are not. I'm a lot less confident that all three of these things would be true of any randomly selected American adult, much less a recent immigrant new to the culture and possibly the language. As Michael Miner summarizes, "Kennedy lets common sense waft him along. Kagan thinks harder."

Along with being an incisive thinker, Justice Kagan is a member of a minority faith. So are two of the three justices who joined her dissent. As for the majority, it's Kennedy and four other Christians. Of course, they're all Catholic—a tradition that was hardly beloved by the founders of the American tradition Kennedy invokes. (A couple weeks after the John Adams letter Justice Kennedy cites above, Adams wrote his wife again: America's future second president had visited a Catholic church with its first, and he found much to mock there.) Yet while the present Court includes six Catholics, only one (Sotomayor) joined Kagan here in expressing some caution about how a government-sanctioned public prayer to the majority's God might affect citizens who practice minority faiths.

Kagan's concern for religious minorities is a lot more persuasive than Kennedy's concern for the legislative-prayer tradition in which all citizens are presumed to be well read. To be clear, I don't find much to like about the more generic sort of prayer the case's losing side called for—the respondents actually referred favorably to the phrase "generic God." What was at stake here wasn't whether legislative prayer should exist at all, but how narrowly to define the parameters within which it is acceptable. And yes, a more strictly nonsectarian prayer—one that's required to invoke only a generic God—can certainly cheapen the concept.

But so does using prayer to bless a government function in the first place. And if preventing Christian ministers from being specific made them lose interest in offering their services at all, I would see this as a positive development. News reports have tended to frame this Court decision as a win for Christian prayer and a loss for religious minorities. I see it as a loss for both.