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Perhaps the Cairo Declaration's signatories believe that sharia law protects universal human rights adequately, and that the UN's version of universal human rights is an attempt to lump together rights that are truly universal with some "rights" that are culturally specific, dubious, and in some cases downright wrongheaded, in order to stuff them down the throats of other countries?

It makes as much sense to say that the Cairo Declaration "subordinates all human rights to sharia law" as to say that the UNDHR "subordinates all human rights to the will of the UN General Assembly". And characterizing the signing of the Cairo Declaration as "rejecting universal human rights" is exactly opposite of the truth: the Cairo Declaration is an affirmation of universal human rights.