A common misconception of the liberal ideology is that it promotes a secular state. That's true, in part; we liberals do want a neutral government when it comes to religion, but we could care less about what the people themselves want to believe in regards to their faith. But conservatives who are pushing for a higher standard of morality in society often further believe that liberals want a moral-less society, one that abolishes faith and religion outright. Nothing could be further from the truth.
What are liberalism's views on religion, morality, and society? Liberals take a stance that is common among most Americans: let the people choose for themselves what to believe. With regards to religion, a person should be free to exercise their views without restriction from the state or any other force in society, so long as their views don't conflict with the rights of others.
Most liberals don't even mind when religious groups take part in ceremonies on public land or have symbols placed in front of city hall. Liberals do take issue, however, when only specific religions are allowed to place such markers in those areas. A Jew or a Muslim has just as much right as a Christian to place a symbol on public land -- in the eyes of the law, these separate faiths (or any other faiths) should be seen as equals.
Morality, on the other hand, is a touchier subject; while most Americans agree that people should be able to choose for themselves what faith is best for them, when it comes to morality everyone believes their faith or beliefs are best to legislate into law. Most can agree on core issues -- you won't find many who believe murder is an acceptable practice in our society -- but on other subjects, a great debate usually surfaces. What are we do about gay marriage, for instance? What about stem cell research? Or gun control? Liberalism looks at these issues of morality and focuses once again on people's rights. Laws on morality should focus on liberties, not a specific faith's views.
For instance, when looking at laws on gun ownership, we should ask ourselves what rights, if any, would be violated by banning a particular weapon. The right to own a gun is one that even most liberals acknowledge as one that shouldn't be infringed upon. But do restrictions on specific weapons deemed dangerous by society infringe upon that right, or do they in fact protect more Americans from dangerous criminals or accidents in the home? That is the debate we should be having with gun rights; it's not an "all-or-nothing" question of whether we should own guns or not, but rather whether certain restrictions of weaponry infringe upon the right to bear arms in our country.
Morality should be legislated in a similar way: we should ask, "What rights are removed from a person if this piece of legislation is passed? In what way will a person's livelihood change if this policy is put into law?" If it's a significant change, enough to affect how a person is able to live their lives, then liberals believe that it's an unjust law, one that violates a person's rights.
Ultimately, morality and religious belief are best left for a person to define for themselves. Yes, there comes a time when a certain moral code needs to be legislated over all others to keep order within society -- but this should be done to preserve the rights of everyone, not just a certain group of people. These rights should be derived from a secular source, not one that is religious in nature. In that way, it is applied equally unto everyone as well as justified by a similar structure, one based on rights, over a population.
If a person wants to subject themselves to their personal faith's moral code, then let them; but they shouldn't expect that same moral code to be subjected upon society itself. For that, we need a moral code that allows everyone the right to make that decision, to decide for themselves what's best for them, while still preserving the rights of the people.