The antonyms for the word "more undiscerning" could be "discerning", "perceptive", "judicious", "sensible", "intelligent", "astute", "wise", "shrewd", "perspicacious", and "clever". These words denote an ability to make sound judgments and decisions, based on careful observation and analysis. An undiscerning person, on the other hand, is one who lacks the ability to distinguish between good and bad, right and wrong, or true and false. They may be easily influenced by others, fall prey to scams and frauds, or simply make poor choices due to their inability to see the bigger picture. Therefore, it is essential to cultivate discernment and critical thinking skills, in order to avoid being undiscerning.