The idea of religious liberty was, for a long time, uncontroversial common ground between right and left. The idea of a private sphere that government must respect—an idea at the core of the gay rights movement—has its roots in dissenting Protestantism. It became the basis for the practice of religious exemptions from generally applicable laws. As recently as 1993, Congress almost unanimously enacted a federal statute codifying that practice. That law continues to produce results that liberals admire, protecting prisoners from arbitrary treatment and religious minorities, notably Muslims, from discrimination. If you want to protect the right to be different, this is a good place to start.
Civil Rights for Whom?: Gay Rights versus Religious Freedom