The phrase "skeptical public" means that people have doubts or are unsure about something. They might question or distrust information or ideas until they have enough evidence to believe in them. Full definition
You miss the point, playing down such errors as being minor reveals to a growing skeptical public that scientists are in denial over their collective failings in presenting climate change. (blogs.nature.com)
«An increasingly skeptical public wants to know the expertise, enterprise and ethics behind a news story. (techcrunch.com)
In the last few days, the new set of tougher math and English language standards for grades K - 12 has suffered a spate of bad publicity that could undermine its very purpose — and turn off an already skeptical public. (hechingerreport.org)