Sadly, I have no explosive tale of rioting monks or clerks to tell. To understand why, we have to explore the dynamics of textual production and consumption in the 15th-16th centuries.

When we think of prints and manuscripts today, we think of books--the Gutenberg Bible, the Book of Kells. Before and after the invention of movable type, full-length books represented a very small percentage of the texts being produced and used. Eight-page pamphlets on how to pray, one-page broadsides predicting the end times, half-sheet certificates of indulgences held up most of the consumer market.

But by far the epicenter of text production came from secretaries in Church and secular chanceries, churning out letters and recording financial transactions and keeping the minutes of university faculty meetings. Most private scribes in cities, too, would have supported themselves primarily with such tasks. You'd hire a notary scribe to write out the insurance agreement you made with a merchant, for example.

In cases like those, the important factor to consider is volume. Scholars estimate that an edition of a printed text, after the rough early years, would produce 500-1000 copies. There is not a market for 500 copies of your deal with the spicer: no printer would take on the time and expense of printing a text with a market of maybe two. Because the majority of text production was ad hoc cases like this, scribal activity hardly faded away in the wake of the printing press. Indeed, as governments came to rely more and more on record keeping and bureaucracy, palace secretaries had even more work. The first postal service in post-Roman Europe arises in the HRE under Maximilian and then Charles V. It runs on individually-copied letters that needed to fly up and down the Empire.

But even in areas like actual book production, there was enough of an overlap/transition period that scribes weren't put out of work. Although in general Europe (at least HRE, the context I know) embraced the printing press, some lingering attitudes saw manuscript production as artistically and maybe even spiritually better. We see this play out most visibly in the way early printed texts tried their very very best to imitate manuscript form and format. With the letter options for type limited and the desire to replicate the ornate initials and decorations of illuminated manuscripts, printers in the early decades would leave blank spaces for scribes to fill in once the ink dried. (Replicating, by the way, manuscript production step-by-step.) And vice versa, the woodcut illustrations so associated with early print gradually took over painted illuminations in manuscripts as well!

Thus, we still find full and partially handwritten books well into the early modern era. And it's important to note that commercial book production required a specialized set of writing and even artistic skills that not all scribes would have possessed. Thus, as demand for manuscript books tapered off gradually, up and coming notaries and scribes would simply not have acquired the skill set.

You mention the specific case of monks--and, I will point out, nuns. The majority of monastic textual production was not commercial but in-house. (In Augsburg and Nuremberg--so probably elsewhere--lay people could borrow texts from monastic libraries to read or have copied for themselves!) Convent financial records, library catalogs, charters of financial transactions, community history--again, these are not texts that would find a swelling commercial market.

Although some convents or individual monastic scribes did take book commissions on demand, they generally depended on donations and other activities to support themselves financially. Scholars have turned up a couple of cases where a community invested in a printing press (the nuns of San Jacobus Ripoli in Florence, for example). But that seems to have been as much an attempt to take advantage of the skyrocketing market for consumer texts like those half-sheet indulgences, rather than a desperate search to replace scribal commissions. The nuns earned the right to operate a printing press because they were such successful and reputed scribes.

One place where the impact of the printing press did have financial consequences was on parchment producers. Although paper had entered Europe long before and many later manuscripts were paper, parchment (vellum) had remained the mark of luxury. Early printers often copied this--but quickly found that mass production (1000 copies!) was financially feasible pretty much only with paper. So you had some voices of protest against the rustification of books with the death of parchment, and some parchment manufacturers who had to look for different economic opportunities. (I don't know that much about this part of the story, sorry.)

Of course, it wouldn't surprise me if frustrated and overwhelmed scribes occasionally vented their feelings about the "ease" of textual mass production with the early modern equivalent of get-off-my-lawn. But overall, the transition was gradual enough, the exponentially increasing demand for texts high enough, and the responsibilities of scribes diverse enough to limit if not completely eliminate the labor pains of print.