There is an alternative view, however, that the old order had used religion to bolster itself, and when rationalism started to show religious beliefs to be questionable, the political system associated with it came under immediate suspicion. According to this narrative, the reactionary case must be made on a rationalist foundation, or else it is always in danger of being undercut again.Indeed. BUT...I'm making an even deeper argument. I claim that authority and reason are fundamentally and deeply opposed concepts.
To lay it out carefully again...
A belief in authority is a question of what obligation Person A has to obey someone else (Person B's) rules.
A belief in reason is a question of what is true/right.
If one believes that one has a choice of actions between X and Y...and reason says X is right, and authority says Y is right...you have to pick (a) which to do, and (b) which to advocate. If you say...do X, you are exalting reason over authority, and you are undermining authority as well. If you say: do Y...you are exalting authority over reason...and undermining reason. Pick at most one. Even better, authority, to be morally supported, needs to undermine support for reason over authority...which is best done by restricting free speech...which Mill correctly pointed out was the core of idea-exchange.
Authority or Reason...pick one.
Disclaimer: I've never been able to understand authority as anything other than thugs with bigger sticks. At 3, my mom reports that I had already chosen reason over authority...and while physical pain or physical restraint could convince me not to do something I thought was a better idea...authority was 100% unable to convince me it was a better idea.
I personally find folks claiming unilateral (unagreed) authority to be exactly morally equivalent to terrorists. Cooperate while they're watching. Undermine at every opportunity.