The main point seems to be the possibility of cheating. Looking a bit further at the links provided the page you've linked you get North Carolina requires test takers disable MacBook Pro Touch Bar for bar exam [u]:
The board didn't explain its policy, but it's presumably concerned about cheating. The Touch Bar is designed to replace physical function keys with context-sensitive touch commands —a programmer could, however, conceivably write software that would display test answers.
And similar from a vendor of exam software about Disabling the Touch Bar on MacBook Pro:
Exam Administrators will want to ensure that the newest feature included with some MacBook Pro's is disabled before a student begins their exam. By default, the Touch Bar will show predictive text depending on what the student is typing, compromising exam integrity.
Since the specific exam software is currently unable to lock down this feature during exam the feature must be either disabled manually or the system is not allowed for exam because of possible cheating.