There is simply no way to answer this question in an objective way.
One seemingly attractive way to answer this is to say that the government should regulate people’s morals whenever those morals have a clear impact on the overall good of society. However, this is not a tenable criterion. You have mentioned the Progressive Era in your explanation of this question. In that time, the government implemented Prohibition. This would seem to be a good instance in which to legislate morals because excessive drinking can be harmful to other individuals as well as to society as a whole. Yet we see clearly that Prohibition did not work.
We might also say that government should regulate morals whenever “bad morals” hurt specific other people. But here, too, we cannot actually put this into practice. For example, the act of adultery can lead to divorce, thus hurting innocent children in the family. But we surely would not want to make adultery a criminal act.
We could say that the government should never regulate morals. But this is not acceptable either. This would force us to make things like polygamy and the marriage of close family members (so long as they do not procreate, perhaps) legal. We would have no way to ban things that are repugnant to most people.
Thus, we have no good way to say when regulation of morals is acceptable.