"If the state says God does not officially exist, who -- or what -- endows the individual with certain unalienable rights? ......"
Since G*d hasn't been down here in a long time, we shall have to make do on our own. If I may be forgiven for even mentioning his name on FR, the founder of ACLU aptly stated "They have rights who will fight for them".
Unalienable rights exist for all men, but they must be willing to insist on them. The Iraqi people did this in their recent election. Ironically, as the Iraqi's exerted their Unalienable Rights, the Supreme Court egregiously restricted the property rights of Americans
Whether or not one believes G*d gave man rights is not the issue. Is society predicated upon those Unalienable Rights? Is that society's populace willing to fight to keep their Unalienable Rights?
I beg to disagree. A recent film "Timechanger" shows what happens when "the law" is divorced from the "law giver." In this instance "rights" without honoring the "rights endower", will eventually lead to no rights, no legitimate rights, just privileges the State temporarily concedes. Once God is left out of the picture, men take His place.