It's a matter of principle. In fact, just about any principle will do.
...The new conservative campaign for religious exemptions follows a well-established pattern. When advocates suffer defeat and their arguments lose legitimacy, they look for new ways to frame their views, often borrowing from their opponents. Initially, for example, critics objected to affirmative action in the name of “innocent” whites, but when that argument proved insufficient, they reframed their case in the language of civil rights. In 1978 in University of California v. Bakke, Justice Lewis Powell said many of the groups that made up the white majority were also minorities that had faced discrimination, and he appealed to ideals of color-blindness to justify restricting race-conscious efforts to integrate public universities.
Conscience is the new color-blindness. In the debate over same-sex marriage, the opponents at first defended traditional marriage by appealing to moral disapproval of homosexuality. When these arguments began to lose credibility, opponents emphasized the importance of preserving sex-differentiated procreation and parenting. Today many have reframed the defense of traditional marriage as necessary to preserve religious liberty, to promote pluralism, and to avoid discrimination against religious conservatives. Again, conservatives are speaking in the language of civil rights. As Jeb Bush has put it, “People that act on their conscience shouldn’t be discriminated against, for sure.”
This is how RFRA has been drawn into the culture wars. After failing to prohibit abortion and same-sex marriage, conservatives have sought to create religious exemptions from laws that protect the right to abortion or same-sex marriage. Without change in numbers or belief, religious conservatives have shifted from speaking as a majority seeking to enforce traditional morality to speaking as a minority seeking exemptions from laws that depart from traditional morality. If unable to protect traditional sexual morality through laws of general application, conservatives can protect traditional values through liberal frames—by asserting claims to religious exemption and by appealing to secular commitments to pluralism and nondiscrimination.
Conservatives’ claims of conscience in conflicts over abortion and same-sex marriage put liberals on the defensive. After all, don’t liberals still support the free exercise of religion? And if liberals do support religious liberty, shouldn’t they accept the logic of the conservative case? Current controversies seem to confront liberals with two unhappy choices: accept the new claims for religious accommodation or compromise longstanding commitments to conscience and religious liberty. But there is a way out of this thicket. The new claims being made by conservatives today are fundamentally different from the claims of religious liberty that led to the passage of RFRA. These differences are crucial to judging whether and how to accommodate the demands for religious exemption...