If you insist on a word, please say so. Else, could a phrase be acceptable?
If you think any belief, or change in belief has anything to do with ‘rapid obedience’ please explain what and how…
If you think anyone or anything being ‘tractable’ or ‘expedient’ has to do with ‘rapid obedience’ please explain…
Respect to Drew and ‘reflexive’ doesn’t mean ‘reflex’. If it did, I suggest physiology has nothing to do with grammar or semantics… ‘Obedience’ involves cognition in a way Pavlovian reflex, ‘rapid’ or otherwise does not. Similarly neither ‘submissiveness’ nor ‘training’ could really be relevant.
I suggest there is nothing remotely like any word meaning anything like ‘rapid obedience’ but given that any kind of qualification of ‘obedience’ makes the question less about the outcome and more about the manner of achieving that outcome, ‘alacrity’ would fit much better than anything else.