What would Posner do if he lived in a country where the majority wished to censor the newspapers, or forbid certain religions, or suspend habeas corpus? Clearly he believes abortion is a negotiable right, but I suspect one wouldn't have to dig very deep to find that other rights were not subject to the vote.

Focusing only on the rights that are obscure, disputed, or otherwise negotiable privileges democracy at the expense of individual rights, which ought not to be subject to a vote.

So because the majority believes that something is wrong (or right) because of their personal religious conviction the minority who does not share that conviction must nonetheless live their lives according to that conviction of the majority? It's a thorny issue but in most cases shouldn't religious freedom include freedom from the religious lifestyle of the majority as well as the right to worship (or not) according to your own desires?

Posner does presumably believe that some rights are nonnegotiable if you want a liberal democracy, but he would also point out that in many cases it's simply not realistic to expect the majority will to be thwarted by a legalistic elite in every case. He'd make that statement without attempting to evaluate its moral implications, of course, because it appears likely that if a substantial majority of people believe X, then a minority that believes not-X, or whose behavior threatens X, will have a difficult time changing the majority's mind. Clearly, this is a complicated set of discussions. (Further, given Posner's positivism, I wonder how much we should discuss "rights" at all.)

That democracy and liberty are often in conflict is not a novel observation, but it is no less true for being commonplace. And some of the behaviors you mention as being undesirable as government policy are nonetheless manifest as a practical matter: The government in this country allows for the publication of staunchly Marxist newspapers, but practically nobody reads them; and we have religious freedom, but in the main the United States' religious composition hasn't radically changed in a century.

As it happens, Posner does note in one of the linked pieces that foreign judges and legislatures routinely decide that hate speech is beyond the pale, while in the United States it can sometimes be constitutionally protected. So here, then, we have a fairly positivist interpretation of what the law "should be."

"So because the majority believes that something is wrong (or right) because of their personal religious conviction the minority who does not share that conviction must nonetheless live their lives according to that conviction of the majority?"

This reminds me of a discussion I had in student government, during a heady era of reform when people were proposing redistricting. Somebody pointed out that if redistricting proposal A were accepted, then congressmen B and C would have to run against each other--and because both B and C were good people, the organization would lose. Told of this, the student government president stared at the interlocutor and said, forcefully, "It's an election! Somebody always loses!"

In the same way: Some policies are mutually incompatible. Somebody will always lose an election. Not-A and A cannot coexist.

The comments that laws against abortion are based on "religion" is not exactly true. Which religion?

Actually, these laws are based on natural law theory. At least in Catholicism, they mix biblical tradition with Greek logic. And many of these restrictions are found in non European/non Christian societies (abortion is considered wrong in the Chippewa, for example, and abortion is witchcraft/murder in Bantu religion).

The problem with progressive "living" constitution is that it allows the rewriting of traditional ideas at the expense of the latest intellectual fad.

Even the most obnoxious traditions in common law and in major religions have a logical basis: They are the way societies encode the lessons of thousands of years of human experience.
So even laws that seem to be stupid have some validity. For example, there is a website that ridicules the bible, stating "God Hates Shrimp"...yet as a doctor, I know shrimp deteriorates easily, and carries many fecal water borne diseases...and ironically, shrimp is taboo as a food for Bantus...who probably observed the same lessons...