I don't get why you're busting on atheists for not supporting extra-judicial executions on here. Elsewhere you have decried this activity but maybe that's because of who the victims were and not the act itself.
" this begs in my mind the question of whether or not this makes atheistic polities inherently less prone to overt social unrest than theistic ones when faced with (I'll add the qualifier "relatively" here, since apparently we're not fond of certainties) injustice, and whether or not this is a good thing. Any thoughts?"
Doubtful. The most stable polities of this century have been the religious kingdoms on the Persian Gulf coast, who have managed somehow to deprive women and large portions of their non-Arab populations even basic political rights for decades, and not only that have survived the recent 'Arab Spring' revolt unscathed (which begs the question in my mind if these things were completely astroturfed). All the secular republics, by contrast, have gone up in flames.
On the other hand atheistic eastern Europe went up in flames in the late 1980s due to various 'injustices', perceived or real.
More recently major social movements in the US, like the anti-globalization movement, the anti-war movement, and the occupy wall street movement, were led by atheists.
Frankly religious people only come out to side with state power, not the other way around.