J. S. Mill is well known as an intellectual father of both Utilitarianism and Liberalism, but I was thinking recently about a tension between these lines of thought and wondered if he ever addressed it. The tension is this, Utilitarianism leaves no boundary between ethics and politics. An action is good if it maximizes happiness, period. Politics, according to a Utilitarian, is just another means of happiness maximization. Liberalism, on the other hand, places a lot of importance on the distinction between public and private behavior and beliefs. So, for example, if I believe in God or not is no concern to others because it is a private belief, but if I rob my neighbor, I am liable to punishment, since this is a public act. However, if Utilitarianism erases the ethics/politics boundary, how can Liberalism keep the public/private boundary in tact?
The most straightforward answer to this question, one which I suppose Mill to have given, is that respecting a public/private boundary in our politics tends to maximize general happiness. After all, as Jefferson said, it neither breaks my leg nor picks my pocket if my neighbor has different religious beliefs. But if the state were seriously committed to happiness maximization, shouldn't the state be obliged to hinder the spread of religions that cause unhappiness? I suppose Mill would say that the marketplace of ideas will ensure that unhappy religions die out in the long run, but isn't that being a bit optimistic? Besides, as Keynes said, in the long run we're all dead. Shouldn't the government try to speed this process along?
So, my question is, does Mill ever make arguments for the public/private distinction that will hold even if it empirically turns out in certain cases that happiness could be maximized by violating this principle? Or were all his arguments for Liberalism empirically grounded? (Although, now that I think of it, you could say the same about any other 'right' guaranteed by liberalism, but I'm especially interested in the public/private distinction, since it is what separates Liberalism from totalitarianism.)