Good moral characters makes a good society. I think it would be good idea to have government regulate public morals. Even thou its in people's hand to build up their personality. If government would set some standards to it people would enforce it, which would build up the standard moral that can create a good society.
The government should absolutely not regulate public morals. Morals are up to that individual, and cannot be governed by any outside entity. It is foolish to think that the opinions of lawmakers will be able to influence any individual with laws. If someone is going to do something, it is highly unlikely that laws are going to stop them.