How should an ideal modern constitution treat religion?

(Originally posted by Jason in 8/2012)

In all honesty, this post is motivated by a recent conversation between Christian and Atheist members of our group regarding Chinese policy towards religion. Apparently, we are in agreement here: people should have the freedom to practice religion, without state's interference. In contrast of the current situation in the US, however, it seems to me that neither country's approach is ideal. It is in fact arguable that US Constitution is not completely secular.
The current US Constitution can be best described as agnostic. In particular, the First Amendment reads:

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

In its historical context, this is probably the best approach it could take, as the original US Constitution and the subsequent Bill of Rights were written before the discovery of most of the modern knowledge and predate Origin of Species by decades. Looking back given what we know, however, such agnostic approach constitutes false balance: it doesn't assert, declare, or promote one position versus the other in the presence of evidence. As we collectively accumulate knowledge, gain power through technology, and more phenomena become predictable, what the public considers "fact" or "truth" only becomes more important over time. Essentially leaving knowledge and empirical approach out of the constitution leaves a nation too susceptible to anti-intellectualism and religious enterprise that has no interest in empirical knowledge or fact.
There are many possible ways to put that into constitution, and it doesn't even have to mention science. For example (this probably fits best in the preamble), "We value subjective experiences but seek and believe in empirical, verifiable facts. We hold it as self-evident that no human had, has, or will ever have inherently unique access to truth over other humans..." Such approach may be considered scientific, but it's not even inherently atheist. If it turns out that super-intelligent beings created the first cell on Earth and finally decide to show themselves, by such constitution we should consider them our Creator, of sorts.  The same goes if it turns out that this universe is a simulation, or some super-intelligent beings (at a totally different level) created this universe and picked some kind of extended combination of Standard Model and General Relativity as its physical laws.
All the subsequent problems aside, taking no position with respect to truth and knowledge is without doubt one secular approach. But while US constitution is not allied with any particular religion, the First Amendment goes out of its way to grant a special kind of freedom to all religions, and religions collectively do not deserve such vaulted position over other schools of thoughts or enterprises. As long as the constitution protects other freedoms like freedom of speech and freedom to assemble, religious practices should be as protected as they should be already. Going out of its way to grant special freedom to religions shields dubious practices that probably won't be allowed under other circumstances from public discourse: if parents want to cut off a part of their child without medical reason, I doubt many people would tolerate such practice in general. Yet, in the context of religious freedom, such position is suddenly controversial: as Wall Street Journal puts it, The German Judge vs. Genesis 17:10. The same shielding effect is also emboldening parents to force their child to attend religious school, a situation that's really violating the child's freedom.
We are essentially out of places on earth to create a new country, but countries rise and fail all the time on the historical scale. Along the line of Paul Gauguin and E.O. Wilson's new book, perhaps one day there really will be a new country, whose constitution opens with a kind of Emancipation Proclamation for Homo sapiens:

We value subjective experiences but seek and believe in empirical, verifiable facts. We hold it as self-evident that no human had, has, or will ever have inherently unique access to truth over other humans...
...We know where we come from, we know who we are, and we will decide where we are going together.