I see something like epistemic conscientiousness as almost the highest value, only potentially surpassable by what I will broadly call concern for others. This principally involves a commitment to understanding, which means always seeking deeper and better and more nuanced understanding. But equally, it involves taking strong personal responsibility for our acceptance of claims.
If I have accepted a claim — especially if I have acted on the basis of that acceptance, or encouraged others to accept it — and then encounter reason to question that claim, I have a responsibility to resolve the matter in some appropriate and reasonable way. If I accept a claim, I have a responsibility to also accept its consequences. I have a responsibility not to accept materially incompatible claims.
An epistemically conscientious person will also naturally care about the acceptance of claims by others. Particular concern for particular others will naturally tend to accentuate this. We also want to treat those others with respect and kindness, and combining this with questioning claims they have accepted can be delicate. (See also Things Said; Honesty, Kindness; Intellectual Virtue, Love.)