The concept of relative morality seems to make perfect sense to secularists, but they'll find that it falls apart under scrutiny every time it is put under the lens of history. Morality is objective and the basic principles of how it operates is the same from society to society, but in many cases it is a very personal definition for us to find ourselves as conscious beings through religion, spirituality, or otherwise.
You cannot legislate morals because of the extremely personal nature of morality. Even if you have a large group of people that agree on a shared moral code, you will have people who disagree and their opinions should be respected. If you can prove criminality or harm then by all means prosecute but if it only "feels" wrong then you have nothing substantial to argue in court.
The only thing legislation does is make immoral things illegal. And even when you define moral, it's very abstract and what morality is varies from person to person. So no, I do not think it is possible to legislate them at all. This would be nearly impossible, if not completely.
In our society, there are too many beliefs and lifestyles for government to legislate morals. In the Catholic religion, it is immoral to take birth control. Though in other religions it is not. With varying religious morals people try to adhere to, legislating morals would probably be in direct conflict with one or more religious groups beliefs. It also steps on rights of Americans to lead their life without interference from the government.