You have a set of conflicting authoritative opinions on important moral issues. You have a particular case in which you need to come to a conclusion. What would you do?
* If you hold that any opinion with at least some probability may be followed, you are a laxist.
* If you hold that the less safe opinion can be followed only if it is solidly probable, but that if it is you can follow it even if the safe opinion is more probable, you are a probabilist.
* If you hold that the less safe opinion can be followed only when you are uncertain about the general principle involved and the less safe opinion is reasonably close to being equal in probability to the safe opinion, you are an aequiprobabilist.
* If you hold that the less safe opinion can be followed only if it is more probable than the safe opinion, you are a probabiliorist.
* If you hold that the less safe opinion can be followed only if it is strictly certain, you are a rigorist (also called a tutiorist).
These could all be formulated in terms of liberty and playing it safe: a laxist holds that you are at liberty to follow any opinion that is probable; the others gradually increase the field in which you are required to play it safe. Strictly speaking, they have all traditionally only applied to ordinary moral cases capable of doubt; they were not supposed to be applied to cases in which personal rights are at stake (on the principle that you should always play it safe with what is due to someone else) or in any other case where it would be simply irrational not to play it safe (for instance, in matters of eternal salvation). But in other cases, they would come into play. Naturally, they don't conflict except in cases where (1) there are conflicting authorities; (2) of varying safeness; (3) and you are considering whether you can follow the less safe opinion.
The biggest casuistical dispute of all time was the dispute between the Jesuits (who were largely probabilists at the time) and the Jansenists (who were unanimously rigorists). One product of that dispute was Pascal's famous Provincial Letters, a merciless but beautifully-written satire of Jesuit probabilism. Pascal, of course, was a major defender of Jansenism. The dispute between the Jesuits and the Jansenists so absorbed philosophical reflection on casuistry that the whole field was in an uproar for nearly two centuries as a result. It is from this dispute that the word 'casuistry' got its bad name.
Whether one likes it or not, casuistry is not the sort of thing you can simply reject; it is simply the rational application of general principles to particular cases, and is essential to moral reasoning. The most important Catholic casuist is Alphonsus Liguori (1696-1787). The most famous Protestant casuist is Richard Baxter (1615-1691), the Puritan, who wrote several works on the subject (you can find them by clicking on the link and scrolling down).
(Cross-posted at Houyhnhnm Land.)