Let's begin this post with a quick definition from Burton's Legal Thesaurus, 4th edition:

civil libertiesnoun First Amendment guarantees, First Amendment Rights, freedom of expression, freedom of press, freedom of religion, freedom of speech, freedom of thought, fundamental individual rights, guarantees from the Bill of Rights, human rights, individual rights, right to life, right to peacefully assemble, right to petition government for redress, right to privacy, right to property, right to worship

There are better definitions, but you get the gist. Freedom of speech is a civil liberty. Freedom of religion is a civil liberty.

Now let's check out this Associated Press story headlined "Arizona House passes bill protecting religion."

The Arizona House has passed a measure that would expand religious freedom protections...
Senate Bill 1178 would allow people to sue over potential violations of religious liberty. Civil liberties groups say the bill would be a nightmare for businesses because it could prompt a wave of lawsuits over alleged First Amendment violations.
Arizona law and the U.S. Constitution already protect religious freedom, but proponents say stricter language is needed.

Beyond the fact that the headline confuses religious liberty with religion and that this is basically the entirety of the article and that the article provides us no context for itself, how about that line that begins "Civil liberties groups say ..."

In an era where journalists are ignorant of religious liberty debates, downplay them, scare quote them, or otherwise, consider this a simple public service announcement that religious liberty is a civil liberty.

If a group is fighting against that particular civil liberty, even if it calls itself a civil liberty group, work to phrase this one better.