Related: What Do We Mean By "Rationality?"
Epistemic rationality and instrumental rationality are both useful. However, some things may benefit one form of rationality yet detract from another. These tradeoffs are often not obvious, but can have serious consequences.
For instance, take the example of learning debate skills. While involved in debate in high school, I learned how to argue a position quite convincingly, muster strong supporting evidence, prepare rebuttals for counterarguments, prepare deflections for counterarguments that are difficult to rebut, and so on.
I also learned how to do so regardless of what side of a topic I was assigned to.
My debate experience has made me a more convincing and more charismatic person, improved my public speaking skills, and bolstered my ability to win arguments. Instrumentally speaking, this can be a very useful skillset. Epistemically speaking, this sort of preparation is very dangerous, and I later had to unlearn many of these thought patterns in order to become better at finding the truth.
For example, when writing research papers, the type of motivated cognition used when searching for evidence to bolster a position in a debate is often counterproductive. Similarly, when discussing what the best move for my business to make is, the ability to argue convincingly for a position regardless of whether it is right is outright dangerous, and lessons learned from debate may actually decrease the odds of making the correct decision-- if I'm wrong but convincing and my colleagues are right but unconvincing, we could very well end up going down the wrong path!
Epistemic and instrumental goals may also conflict in other ways. For instance, Kelly (2003) points out that, from an epistemic rationality perspective, learning movie spoilers is desirable, since they will improve your model of the world. Nevertheless, many people consider spoilers to be instrumentally negative, since they prefer the tension of not knowing what will happen while they watch a movie.
Bostrom (2011) describes many more situations where having a more accurate model of the world can be hazardous to various instrumental objectives. For instance, knowing where the best parties are held on campus can be a very useful piece of knowledge to have in many contexts, but can become a distracting temptation when you're writing your thesis. Knowing that one of your best friends has just died can be very relevant to your model of the world, but can also cause you to become dangerously depressed. Knowing that Stalin's wife didn't die from appendicitis can be useful for understanding certain motivations, but can be extraordinarily dangerous to know if the secret police come calling.
Thus, epistemic and instrumental rationality can in some cases come into conflict. Some instrumental skillsets might be better off neglected for reasons of epistemic hygeine; similarly, some epistemic ventures might yield information that it would be instrumentally better not to know. When developing rationality practices and honing one's skills, we should take care to acknowledge these tradeoffs and plan accordingly.
 Kelly, T., (2003). Epistemic Rationality as Instrumental Rationality: A Critique. Philosophy and Phenomenological Research, 66(3), pp. 612-640.
 Bostrom, N., (2011). Information Hazards: A Typology of Harms from Knowledge. Review of Contemporary Philosophy, 10, pp. 44-79.