"The state which we seek can never be presided over by a non-Muslim," said Mohammed Morsi, who drafted that platform and is now president of Egypt.
Maybe Morsi still privately thinks that, or maybe he has realised that these rules are unacceptable in a democracy where all citizens are equal. It doesn't matter.
The new constitution does not contain any such provisions, and the main reason is obviously the Brotherhood's tacit bargain with the armed forces.
The deal, which guarantees the military's privileges, was necessary to persuade the staunchly secular armed forces to accept an Islamic party in government, but it had a price: the new government could not be too Islamic.
This posed a problem for Morsi, because Muslim Brotherhood activists wanted to use their political power to entrench "Islamic" rules in the new constitution.
So Morsi had to walk a fine line. He had to put enough Islamic language into the constitution to mollify his own supporters, but not so much that the military would break their alliance with him. He didn't walk that line very well.
The whole constitutional process was a poisonous battle even before Morsi became president last June. In April the Supreme Judicial Council, whose members had all been appointed by the Mubarak dictatorship, dissolved the newly elected House of Representatives on a flimsy pretext, and also dismissed the constitution-writing assembly that it had chosen.
But the upper house of parliament is also dominated by Islamist parties, and it simply appointed another constituent assembly with the same make-up. After that it was open war.
By October most of the non-Islamists in the second constituent assembly had walked out, and the Supreme Judicial Council was about to dismiss that body too. Morsi's clumsy response was to grant himself unlimited powers and forbid the judiciary to dismiss the assembly.
There was an outcry by the opposition, a fractious coalition of leftists, liberals and Christians, and the protesters were instantly back on the streets. But the constituent assembly promptly rendered the whole crisis unnecessary by passing the new draft constitution in a 29-hour marathon sitting, so Morsi cancelled his special powers - and on December, 22 Egyptians ratified the new constitution by a 63.8 per cent majority.
Small crisis, not many hurt. The army got what it wanted: henceforward, the minister of defence must be a serving officer, and the military will effectively control its own budget. The parliament cannot even debate it.
The Brotherhood got less of what it wanted, but there are bits of Islamic language in the constitution to keep the activists happy. For example, Article 2 of the old constitution (1971) says: "The principles of Sharia are the main source of legislation." Putting that in would have required a major battle with the misogynist rank and file of the Brotherhood, and the old formula would be quite adequate if the courts enforced it. The new one still says that, but Article 219 adds: "The principles of Sharia include general evidence and foundations, rules and jurisprudence as well as sources accepted by doctrines of Sunni Islam and the majority of Muslim scholars." And what practical difference does that make?
Article 30 states that "citizens are equal before the law and equal in rights and obligations without discrimination," but as in the old constitution, there is no separate and explicit guarantee of women's rights. Putting it in would have required a major battle with the misogynist rank and file of the Brotherhood, and the old formula does the job perfectly well.
Nervous secular Egyptians fear that these bits and pieces of Islamic rhetoric are the seeds of a constitutional revolution that will turn the country into an Islamist dictatorship, but there is little evidence for that.
As for the frantic haste with which the constitution was passed - after two years of revolutionary upheaval, the Egyptian economy desperately needs the political stability that a new constitution and fresh elections (due in February) will provide. It's not a plot. It's just the politics of necessity.
Gwynne Dyer is an independent journalist whose articles are published in 45 countries.