I long ago read, and have ever since remembered, that "irreverence can never be separated from impiety": so far as I recalled, Trent said so somewhere in regards to the sacred liturgy.
Well, thanks to the relevant quotation having just featured in a posting at The Anglo-Catholic blog, I have finally sourced it, and moreover have found the Latin original, in the Decretum de observandis et evitandis in celebratione missæ [Decree about things to be observed and things to be avoided in the celebration of Mass], which the Council of Trent passed on the l7th September 1562:
“The local ordinaries shall be zealously concerned and be bound to prohibit and abolish all those things which either covetousness, which is a serving of idols, or irreverence, which can scarcely be separated from ungodliness, or superstition, a false imitation of true piety, have introduced."
...ut ordinarii locorum episcopi ea omnia prohibere atque e medio tollere sedulo curent ac teneantur quae vel avaritia idolorum servitus vel irreverentia quae ab impietate vix seiuncta esse potest vel superstitio verae pietatis falsa imitatrix induxit.
There it appears: "irreverence, which can scarcely be separated from impiety" – irreverentia quæ ab impietate vix sejuncta esse potest – or, "irreverence, which from impiety is scarcely able to be separated". I have remembered this almost right, but "scarcely" is more accurate than "never".
Irreverence is scarce separable from impiety.