The Washington Post:

In his dissent, Chief Justice John Roberts Jr. discussed religious liberty concerns. “Today’s decision, for example, creates serious questions about religious liberty,” Roberts wrote. “Many good and decent people oppose same-sex marriage as a tenet of faith, and their freedom to exercise religion is—unlike the right imagined by the majority— actually spelled out in the Constitution.”

“Hard questions arise when people of faith exercise religion in ways that may be seen to conflict with the new right to same-sex marriage—when, for example, a religious college provides married student housing only to opposite-sex married couples, or a religious adoption agency declines to place children with same-sex married couples. Indeed, the Solicitor General candidly acknowledged that the tax exemptions of some religious institutions would be in question if they opposed same-sex marriage. See Tr. of Oral Arg. on Question 1, at 36–38. There is little doubt that these and similar questions will soon be before this Court. Unfortunately, people of faith can take no comfort in the treatment they receive from the majority today.”
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Alito wrote in his dissenting opinion: "The majority attempts, toward the end of its opinion, to reassure those who oppose same-sex marriage that their rights of conscience will be protected. We will soon see whether this proves to be true. I assume that those who cling to old beliefs will be able to whisper their thoughts in the recesses of their homes, but if they repeat those views in public, they will risk being labeled as bigots and treated as such by governments, employers, and schools."