I would disqualify anyone who was evasive.
Even a little bit.
Outright lies and you should be charged with a crime.
Why don't you disassociate and compartmentalize and keep character out of the picture?
I don't hold hypocrisy as remotely relevant. Only a subset of character is critical. Will he perform as commensurately as duty demands? That's the key. What are the functional characteristics not merely expected but specifically demanded of the position? To judge in unbiased fashion?
To discrimate exactly where it's called upon to do so. I expect impartiality, unpredjudicedness, neutrality, a nonpartisan bent, strong willed intent to remain disinterested, or detached even, dispassionate, objective, value-free, open-minded, equitable, even-handed, fair where fairness is called for.
So, to that end, what's with all these character related expectations? It's when you're up to bat that I expect a batter to perform--not to hold a grudge like a fan shows towards a disgraced actor.
When I watched America's got talent or Dancing with the Stars, it was the performance that I felt deserved judging, not the backstory of the hurdles overcome, not the affiliation to the military and their service (to which is appreciated either way) and not the heartfelt tear-jerking intentions reflective of their character.
If I need someone to hold a sign up to deal with traffic (signs of past cowardice in the face of danger might make a difference), if I need a person to ensure money gets to the bank (signs of untrustworthiness with money might make a difference), but I don't need a sober judge to remain indifferent and blast drunk drivers. I hope he is a hypocrite. I expect hypocracy. Do your job.
You speak of disqualifying someone even for evasiveness. I was on the fence with lying under oath, but not even honesty (in all instances in all venues) is a necessary ingredient for being an absolutely astounding great judge. What he does when up to bat is where the proof is in the pudding.
I'd feel more relaxed being amidst one with great values of honesty and honor--and might even consider taking subpar skills for it, but this world is nothing but full of people that are full of shit. Eyes wide open, we should know this in heart of hearts.
Integrity. It's nice to affiliate ourselves with those capable of espousing that they have it and respect it, but when they are no better, put before me a judge that can at least judge well. Yeah, he may have fingered someone or whatever the hell they said, and you want what (?), someone that will not only be truthfull but not even for a moment hesitate or be evasive to a question posed to him? That's why exactly? The value of honesty, integrity, and honor are values that Trump our second rate skills? Sounds reasonable ... until they too are nothing but a faced.
Your view is admirable. Mine, despicable, if I actually held it. I try to be cautious and not generalize, but it's most (and not merely many) members of our species that have proven time and time again that trust is as fleeting as the wind.