I think what gets me here is that these individuals (by whom I don't mean all religious people, or all Catholics, but those of this particular mindset) are not recommending disobedience to laws that send people to war, or perpetrate economic injustice. Or even for the most part, those which contradict Catholic social rules as a whole. They are not mostly, for example, recommending that Catholics refuse to co-operate in the civil remarriages of divorced people, or that they refuse to vote for politicians who support capital punishment. They are obsessed with restricting the rights of gay people, or women's reproductive rights, or both. Therefore they seem to be more preoccupied with their own rights to be harsh and authoritarian toward certain groups of people, than with preventing war or poverty, or even with promoting social conservativism in areas that could affect straight males.
Once again: there are plenty of religious people who do campaign against war, poverty, and cruelty; but most of the religious right do not. And although we're talking about Catholics here, it applies to hardliners in many faiths.