They are not, moreover they can be modulated and both positively interact (in fact, the vast majority of creative people have had and have very good self-control: the relationship between creativity and emotional instability and, even, psychopathological disorders and insanity IN A STEREOTYPE UNFUNDED AND A MYTH.).

Are creativity and inhibitory control mutually exclusive?

yes,

Creativity is the ability to generate, create, or discover new ideas, solutions, and possibilities. divergent thinking: the opposite of convergent thinking, the capacity for exploring multiple potential answers or solutions to a given question or problem (e.g., coming up with many different uses for a common object) .

Broadly speaking, inhibitory control is the ability to suppress the activation, processing, or expression of information that would otherwise interfere with the efficient attainment of a cognitive or behavioral goal(Towards creativity here).

We doubt the importance of response inhibition for optimal and goal-directed behaviour. Without the ability to stop habitual or no-longer relevant actions, we would be slaves of our past; we would be impulsive creatures that respond to any potentially relevant stimulus that presents itself; and we would not be able to respond adequately to changes in the environment. Quite often, this would lead to terrible outcomes. One could even say that we would be doomed without inhibition… At least, it seems this way when you look at the pivotal role of response inhibition in current theories of self-control. There is a vast amount of cognitive and neuroscience literature that suggests that response inhibition is one of the core ‘executive’ or ‘cognitive control’ functions (Logan, 1994, Miyake et al., 2000, Ridderinkhof et al., 2004, Verbruggen and Logan, 2008d) .

so i agree Principally creativity and inhibitory control are mutually exclusive.

you can refer to the following research links :

Article The inhibitory control reflex

Article Differential effects of cognitive inhibition and intelligenc...

Article The relationship between the development of response inhibit...

https://www.ideastogo.com/articles-on-innovation/why-you-should-have-a-child-like-imagination-and-the-research-that-proves-it

hope these are helpful.

best wishes

They are not, moreover they can be modulated and both positively interact (in fact, the vast majority of creative people have had and have very good self-control: the relationship between creativity and emotional instability and, even, psychopathological disorders and insanity IN A STEREOTYPE UNFUNDED AND A MYTH.).

Pretty much nothing in the brain from a neurobiological perspective is mutually exclusive. All these neural circuits that are named in isolation, interact with each other during their activations. Its a common misconception of neural activity that one circuit is activated while another is turned off. A more accurate way to viewing it is that one just happens to be "louder" so to speak in a given context than the others around it. So during a creative task, the areas of the brain associated with those tasks are "louder" and working to drown out the areas that work to inhibit them. And they do that with various neurotransmitters that inhibit neuro activity, but once the context changes that neurotransmitter secretion stops and those inhibited neurons start to activate, and in turn inhibit the circuit they target. That delicate balance of inhibition and activation drives all neural activity. Now as to an optimal level for those kinds of activities specifically in the context of creativity? There's almost certainly an optimal level, but I suspect that will differ slightly from individual to individual. To date and to my knowledge we really haven't managed to quantify that within the field to any degree of accuracy. Being able to state an optimal level for creativity in the context of neurobiology is one part of the holy grail question in all of neurology and psychology. If we get to the point it can be done with creativity, then that technique might be generalized to other attributes, like pure intellectual capacity.

To the second part of the question, "creative geniuses" are almost certainly going to contend with inhibition effects. But whatever neural circuity that they're using for their chosen art/task should be so strongly developed that it shouldn't have much issue overcoming that inhibition. However on the opposing side of that, there's a limit to the "capacity" so to speak of those creative areas of the brain. So eventually those areas will be exhausted and the inhibition areas will take over, reducing problem solving capacity and eventually forcing a break.