Civil liberties are a very partisan issue because the two parties have very different ideas of what constitutes freedom. Both sides are sincerely committed to the idea of freedom, but they do not agree on what freedom entails.
Liberals tend to equate civil liberties with things like gay rights and freedom from religious displays. They feel that freedom refers to the idea that people should be able to behave as they wish without being forced to comply with norms that are linked to specific religious beliefs. They do not want the government to enforce traditional norms and values.
By contrast, conservatives are more likely to feel that freedom involves traditional values. They feel that freedom includes the freedom for cheerleaders to make religious banners at their public schools. They feel that freedom involves the right to carry a gun. These are very different views of what freedom is. This is why civil liberties become a partisan issue even though both parties truly believe in freedom.