She strongly backed expanding it - at the expense of gay rights:

“I’m the biggest fan of [the Religious Freedom Restoration Act] (now [the Religious Liberty Protection Act]) in this building, but you should not take this advice right now,” Kagan wrote in a May 20, 1999 memo to Ron Klain, then the chief of staff to Al Gore, the vice president. “You’ll have a gay/lesbian firestorm on your hands. (Alternatively, if you come out for a version of RFRA that has a civil rights carve-out, you’ll have a religious groups firestorm on your hands.)” ...

Kagan, who worked in the Clinton White House from 1995 to 1999, urged the administration in a 1996 memo to join religious conservatives in asking the US Supreme Court to review and reverse a California Supreme Court ruling that found that a landlord’s religious objections to renting to an unmarried couple were trumped by that state’s anti-discrimination law noting “the danger this decision poses to RFRA’s guarantee of religious freedom in the State of California.”