It’s really quite simple.  Religious liberty means the freedom to believe what you believe, to state or even argue your beliefs in public if you wish, to gather in religious community, to worship as you choose, and to live your own personal life according to your religious faith or perspective.  Religious liberty does not and cannot mean the freedom to violate the rights or freedoms of others, to discriminate or violate public accommodation laws when serving the public, or to impose your religious practices and restrictions on employees, students or customers who may not share your religion.
Fortunately, the Governor of Arizona just vetoed a noxious bill that would have allowed many kinds of public discrimination in the name of religious freedom.  Unfortunately, the idea that religious freedom should allow discrimination and override public accommodation laws has been popping up in many places, including here in Colorado.  The ACLU of Colorado recently won summary judgment against a bakery that refused to make a cake for a same-sex couple in violation of long-standing public accommodation laws.  These laws are essential for equal protection in public commerce, preventing a chaotic breakdown of civility in a society with many different religious beliefs and personal biases.
The ACLU of Colorado upholds true religious liberty for all people and First Amendment principles of both free exercise of religion and non-establishment of religion in the public sphere.  If a bakery or other retail outlet refused to serve someone because of their religious beliefs, including the beliefs of any Christian tradition, we would fight that discrimination, too.  Ironically, the bill just vetoed in Arizona might have allowed exactly that kind of discrimination to occur.  It will be essential to remain vigilant against attempts to justify acts of discrimination against LGBT persons or anyone else in the name of religious liberty.