>>FWIW, my understanding of not just the Bet Din, but Jewish law in general, is that local law prevails. So a Beth Din can't make a ruling that's in violation of the prevailing law of the country where the Bet Din operates.
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>That begs the question as to whether Sharia law operates under the same principle or not...

It doesn't matter. Whoever made the loophole to give one religious court's decisions a legal footing, has opened it for every other such court.