A number of prominent Democrats in the past supported laws similar to the controversial new legislation in Indiana, which says the government can't "substantially burden a person's exercise of religion" in requiring them to engage in business practices or transactions that violate their beliefs. (The classic example in which the law could come into play, of course, is in allowing religious bakers or florists to deny service to a gay couple for their wedding.)
Though this particular bill was backed by Republicans in Indiana, Democrats like President Obama, Hillary Clinton, and Sen. Chuck Schumer have all supported similar legislation themselves. President Bill Clinton signed a similar (though narrower) federal law into effect in 1993, and then-State Sen. Barack Obama voted for religious freedom legislation in Illinois in 1998.
White House Press Secretary Josh Earnest avoided explaining any substantial differences between the laws, arguing instead that the Indiana legislation is outdated.