When someone is skeptical and wants ask questions, it's reasonable to hear them out. When said person fails to listen or accept basic facts (that allow establishing a shared reality), we should turn the volume down on them.

If Tommy, age 7, asks if the Earth is round, teachers should explain how we know the Earth is round and give Tommy a couple of ways to check. When Tommy comes back at age 27, having done no experiments, convinced the Earth is flat, and alleging a massive global conspiracy to hide that fact for domination, we should ignore Tommy. If Tommy persists, the amount of embarrassment and shame they face should be proportional to how loud they are.