"incredibly rigid" is correct and usable in written English.
You can use it when you want to emphasize something is especially stiff and inflexible. Example sentence: The rules of the game were incredibly rigid and could not be altered in any way.
Apart from obscuring scientific facts, it teaches a way of thinking that is incredibly rigid.
"Chuck is a Type A personality, and he used to be, quite frankly, incredibly rigid," Tom told me.
How did America develop these incredibly rigid sports institutions, while in Europe the leagues are just much more freewheeling?
Initially she stated "I focus mostly on time constraints" and "I assign a schedule, it's not incredibly rigid, but it is structured".
"They were incredibly rigid and not at all discreet.
Louis XIV's itinerary was so incredibly specific and rigid that Eliasson has responded with an interactive website displaying a series of drawings that suggest an alternative, non-linear route to experience the gardens.
Over-exercising in a compulsive and rigid way can be incredibly harmful for both your physical and mental health.
Bob Bowman described Phelps as "a solitary man" with a "rigid focus" at the pool prior to a race, but afterwards "a man incredibly invested in the success of the people he cares about".
Like the paintball cheat, Natalya's AI or the hilariously rigid karate chop attack, the Golden Gun sequence is a part of this game's incredibly strong, but not always purposefully styled identity and character.
In an incredibly busy team environment it is difficult to strictly ring fence time, but other professions are much more rigid about the opportunity to engage with a trusted person and examine their own emotional health.
